Statistics and Probability Answers

I'm on an iPad and it wouldn't let me select stats.
Find the sample standard deviation for the following data 15,16,17,18,19
I got 1.5 but I'm not sure if it's correct

The mean amount purchased by a typical customer at Churchill's Grocery Store is $21.00 with a standard deviation of $7.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 42 customers, answer the following questions.





(a)


What is the likelihood the sample mean is at least $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)





Probability







(b)


What is the likelihood the sample mean is greater than $20.00 but less than $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)





Probability







(c)


Within what limits will 99 percent of the sample means occur? (Round your answers to 2 decimal places.)





Sample mean



and

1. A bunch of mixed colored roses has 5 red roses, 3 pink roses, 2 white roses, and 2 yellow roses. What is the probability of drawing a pink rose from this bunch of roses?






2. Consider the experiment of rolling a fair die twice. Find the probability that the sum of the two dice equal 4 and one of the dice is a 3.






3. A couple has three children. What is the probability that they will have 2 of one gender and 1 of the other gender?






4. A Rasmussen report in 2009 gives the details about the support President Obama has for his stimulus plan. The table below gives information about the opinions of 200 Democrats, 200 Republicans, and 100 Independents. Use the table to find the probability that a randomly selected individual is a Democrat or he or she favors the plan.
Favor Opposed Not Sure Total
Democrat 128 21 51 200
Republican 26 144 30 200
Independent 31 50 19 100
Total 185 215 100 500


5. According to the National Lightning Safety Institute, 1 in every 200 households will be struck

a. Construct a scatter plot using Excel or StatCrunch for the given data. B. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. C. Complete the table and find the correlation coefficient r. The data for x and y is shown below.

x 11 -6 8 -3 -2 1 5 -5 6 7
y -5 -3 4 1 -1 -2 0 2 3 -4

a. Scatter plot

b. Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation)

c. Complete the table and find the correlation coefficient r.


x y xy x2 y2
11 -5
-6 -3
8 4
-3 1
-2 -1
1 -2
5 0
-5 2
6 3
7 -4


Use the last row of the table to show the column totals.
n = 10

r =



2. a. Construct a scatter plot including the regression line using Excel or StatCrunch for the given data. B. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. C. Complete the table and find the correlation coefficient r.

a. The data below are the ages and systolic blood pressure (measured in millimeters of mercury) of 9 randomly selected adults.

Age, x 38 41 45 48 51 53 57 61 65
Pressure, y 116 120 123 131 142 145 148 150 152

Part 1: Scatter plot with regression line.

Part 2: Type of correlation (positive linear correlation, negative linear correlation, or no linear correlation)

Part 3: Complete the table and find the correlation coefficient r.

x y xy x2 y2
38 116
41 120
45 123
48 131
51 142
53 145
57 148
61 150
65 152

Use the last row of the table to show the column totals.
n = 9





3. Using the r calculated in problem 2c test the significance of the correlation coefficient using  = 0.01 and the claim rho = 0. Use the steps for a hypothesis test shown. (Note: Round the computed t to 3 decimal places.)

1. H0 :
Ha :
2.  =
3.
4. For degrees of freedom =
5. Rejection region:
6. Decision: Since
7. Interpretation:





4. The data below are the ages and systolic blood pressure (measured in millimeters of mercury) of 9 randomly selected adults.

Age, x 38 41 45 48 51 53 57 61 65
Pressure, y 116 120 123 131 142 145 148 150 152

a. Find the equation of the regression line for the given data. Round the line values to the nearest two decimal places.


b. Using the equation found in part a, predict the pressure when the age is 50. Round to the nearest mm.

Midwestern and Southern households were independently sampled and data collected regarding annual vehicle miles driven (in thousands). Using the data provided, perform an independent t-test using a pooled variance to determine if there is any difference in the two sample means at the .05 level.


Midwest South
Mean 15.23 18.39
Var 4.76 4.12
n 15 18


2. The tread wear of 11 tires is measured using two methods: one is based on the weight of the tire remaining and other is based on the height of the tire grooves remaining. Using a paired t-test (since they are the same tire) and the results in the table for tread wear based on the two methods, is there enough evidence at the .05 level to conclude that there is a difference between the two methods of measuring tread wear?


Tread wear by Tire weight method
(thousands of miles) Tread wear by Groove height method
(thousands of miles)
28.7 30.5
25.9 30.9
23.3 31.9
23.1 30.4
23.7 27.3
20.9 20.4
16.1 24.5
19.9 20.9
15.2 18.9
11.5 13.7
11.2 11.4



3. Firearms leave unique markings on shell casings called ballistic fingerprints. In a survey of 437 woman and 595 men, 396 of the women and 407 of the men supported gun control measures that included ballistic fingerprinting. Use a z-test of proportions to determine if there is any difference in the opinions of the genders on this topic. Use the 0.05 level of significance.

1. Use the method specified to perform the hypothesis test for the population
mean . WeatherBug say that the mean daily high for December in a large Florida city is F. WFLA weather suspects that this temperature is not accurate. A hypothesis test is performed the determine if the mean is actually lower than F. Assume that the population standard deviation of  = F. A sample of mean daily temperatures for December over the past 40 years gives F. At  = 0.01, does the data provide sufficient evidence to conclude that the mean temperature is different than F.

a. Use the critical value z0 method from the normal distribution.


1. H0 :
Ha :
2.  =
3. Test statistics:
4. P-value or critical z0 or t0.
5. Rejection Region:

6. Decision:
7. Interpretation:


b. Use the P-value method to determine if the mean is different than 76 degrees F, but at the .05 level of confidence.


1. H0 :
Ha :
2. 
3. Test statistics:
4. P-value or critical z0 or t0.
Rejection Region:
5. Decision:
6. Interpretation:


2. A local tire store suspects that the mean life of a new discount tire is less that 39,000 miles. To check the claim, the store selects randomly 18 of these new discount tires. When they are tested, it is found that the mean life is 38,250 miles with a sample standard deviation s = 1200 miles. Assume the distribution is normally distributed.

a. Use the critical value t0 method from the normal distribution to test for the population mean . Test the company’s claim at the level of significance  = 0.05.


1. H0 : 
Ha : 
2. 
3. Test statistics:
4. P-value or critical z0 or t0.
5. Rejection Region:
6. Decision:
7. Interpretation:


b. Use the critical value t0 method from the normal distribution to test for the population mean . Test the company’s claim at the level of significance  = 0.01


1. H0 :
Ha :
2. 
3. Test statistics:
4. P-value or critical z0 or t0.
5. Rejection Region:
6. Decision:
7. Interpretation:



3. A flash drive manufacturer has set a standard on their production process. When defects exceed 3%, the production process is unacceptable. A random sample of 300 drives is tested. The defective rate is 5.9%. Use a level of significance of  = 0.01 to test to see if you have sufficient evidence to support the claim that the defective rate exceeds 3%. (Round p-hat to 3 decimal places.)


1. H0 :
Ha :
2. 
3. Test statistics:
4. P-value or critical z0 or t0.
5. Rejection Region:
6. Decision:

1. The new Twinkle bulb has a standard deviation hours. A random sample of 60 light bulbs is selected from inventory. The sample mean was found to be 500 hours.

a. Find the margin of error E for a 95% confidence interval.
Round your answer to the nearest hundredths. .


b. Construct a 95% confidence interval for the mean life,  of all Twinkle bulbs.


2. A standard placement test has a mean of 125 and a standard deviation of  = 15. Determine the minimum sample size if we want to be 90% certain that we are within 3 points of the true mean.



3. An experimental egg farm is raising chickens to produce low cholesterol eggs. A lab tested 20 randomly selected eggs and found that the mean amount of cholesterol was 180 mg. The sample standard deviation was found to be s = 25.0 mg on this group. Assume that the population is normally distributed.


a. Find the margin of error for a 95% confidence interval. Round your answer to the nearest tenths.

b. Find a 95% confidence interval for the mean  cholesterol content for all experimental eggs. Assume that the population is normally distributed.


4. The new Twinkle bulb is being developed to last more than 1000 hours. A random sample of 120 of these new bulbs is selected from the production line. It was found that 90 lasted more than 1000 hours.


a. Construct a 99% confidence interval for the population proportion “p” of all Twinkle bulbs. Round to the nearest three decimals.



b. Construct a 95% confidence interval for the population proportion “p” of all Twinkle bulbs. Round to the nearest three decimals.

A True-False test has 20 questions with each having 2 possible answers with one correct. Assume a student randomly guesses the answer to every question.

a. What is the probability of getting exactly 9 correct answers?


b. What is the probability of getting less than 6 correct answers?




3a. The diameters of a wooden dowel produced by a new machine are normally distributed with a mean of 0.55 inches and a standard deviation of 0.01 inches. What percent of the dowels will have a diameter less than 0.57?



3b. The a loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 50. Find the probability that an applicant will have a rating greater than 300.




4. Answer the questions about the specified normal distribution.

a. The lifetime of ZZZ batteries are normally distributed with a mean of 265 hours and a standard deviation  of 10 hours. Find the number of hours that represent the the 40th percentile.



b. Scores on an English placement test are normally distributed with a mean of 36 and standard deviation  of 6.5. Find the score that marks the top 5%.


5. Find the probabilities.


a. From National Weather Service records, the annual snowfall in the TopKick Mountains has a mean of 92 inches and a standard deviation  of 12 inches. If the snowfall from 25 randomly selected years are chosen, what it the probability that the snowfall would be less than 95 inches?




b. The loan officer rates applicants for credit. Ratings are normally distributed. The mean is 240 and the standard deviation is 60. If 36 applicants are randomly chosen, what is the probability that they will have a rating between 230 and 260?

The length of human pregnancies is bell-shaped with a mean of 265 days and a standard deviation of 10 days. Use the Empirical Rule to determine the percent of women whose pregnancies are between 255 and 275 days.

A box has 4 red balls and 3 green balls. If 3 balls are drawn with replacement, what is the probability of drawing 2 red and 1 green balls?