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On the Standford-Binet test, the mean IQ is 100. A class of 21 kindergarten pupils were tested with a resulting mean of 105 and a standard deviation of 5.44. Does this group have a mean significantly different than the norm group? Use 0.01 as your level of significance.
A random sample of 11 cigarettes of a certain brand has an average nicotine content of 6.6 milligrams and a standard deviation of 2.5 milligrams. Is this in line with the manufacturer's claim that the average nicotine content does not exceed 4.2 milligrams? Use 0.1 level of significance.
According to Dietary Goals for the US (1977), high sodium intake may be related to ulcers, stomach cancer, and migrane headaches. The human requirement for salt is less than 220 milligrams per day, which is surpassed in most single servings of ready-to-eat noodles. If a random sample of 22 similar servings of noodles has a mean sodium content of 210 milligrams and a standard deviation of 5.23 does this suggest at the 0.01 level of significance that the average sodium content for a single servings of noodles is less than 220 milligrams?
b. How long will a call be responded if it has a z-score of – 1.83?
A random variable has PDF p_i = 2(1/3)^i and takes on values in the positive integers. What is the probability that it takes on a value between 10 and 20, inclusive? Show your work step by step.
A math teacher believes that a grade 7 student will get a score of not more than 70 in the 100-item diagnostic test administered last week. To test this claim, the scores of 40 students who took the diagnostic test was recorded. The mean of their scores is 87.65 with a standard deviation of 6. Which of the following test statistic should be used?
Perpetrators of a crime who have been given the maximum sentence of 10 years are believed by a fiscal to have been sentenced to more than 7 years on the average. A random sample of 20 of these crime offenders reveals a mean sentence of 7.6 years with a standard deviation of 2.4 years. Which of the following test statistic should be used?
If the mean and standard deviation of a continuous random variable that is normally distributed are 28 and 3 respectively using the empirical rule find an interval that contains 95% of the distribution
ACTIVITY #4
Scoring system: 1 point for correct answer and 2 points for the solution
A. Use the Table of Standard Normal distribution to determine corresponding probabilities of the following:
1. P(Z < -1.45)
2. P(0.5<Z < 2.33)
3. P(Z > 1.78)
B. X is a normally distributed random variable with a mean of 60 and a standard deviation of 8. Find the probabilities indicated by using the table.
1. P(X < 52)
2. P(48 < X < 64)
3. P(X > 57)
C. Solve the following problems by supplying the needed information.
The average number of calories in a 1.8-ounce chocolate bar is 230. Suppose that the distribution of calories is approximately normal with a standard deviation of 10.
1. Find the probability that a randomly selected chocolate bar will have less than 200 calories.
2. Find the probability that a randomly selected chocolate bar will have greater than 195 calories. 3. What is the percentage that a chocolate bar is randomly selected between 200 calories and 250 calories?
Activity #5
2. The scores of the 5 randomly selected HUMSS students are given below:
26
45
31
लल 34
34
44
47
23
44
38
Complete the table and compute for the sample mean, sample variance, and sample standard
deviation,
Student's No.
Scores (x)
2
3
4
3
£x =
Write your computations here
sample mean
sample variance
sample standard deviation
29
E = mc²
