Statistics and Probability Answers

Three swimmers in 100m race, swimmer A is twice as likely to win as B and three times as to win as C. Find the probability that B or C wins. show us workings

Let is observed the height (cm) of the students in a school, and sample with size of 40 students is consider:
165,185,172,151,164,151,169,176,166,178,178,166,158,
165,151,172,184,174,158,172,164,151,169,176,166,178,
176, 158, 152,165,172,186,174,158,184,170,152,164,161,166.
After grouping the data into 6 class intervals with equal width:
a) Make a summary table for the grouped frequency, grouped relative frequency and “less than” grouped cumulative frequency distribution for the given data.

The restaurant Exclusive advertises delivery of ready prepared food. The announcement states that ordered food will be served for less than 50 minutes from receiving the order. Based on a random sample of 100 orders the average time for delivery of orders is calculated to be 49 minutes, and standard deviation of 5 minutes. What can be concluded on this random sample about the time of delivery with acceptable risk ?

Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3, we perform the following hypothesis test.

Ho: μ = 750
H1: μ < 750

What is the conclusion of the test at the σ= 0.10 level? Explain your answer.

(a) The table given below shows the nutritional and cost information for the meat (fish) and vegetable (spinach)

Per unit of fish Per unit of spinach Minimum requirement
Units of vitamins 5 1 13
Units of protein 10 3 16
Unit cost Rs. 50 Rs. 20

Find a diet (i.e. units of vitamins and proteins) to meet the minimum nutritional requirement at minimum cost.

Mr. Fox is not the kind of person who rests. He and Batman get back to business. He is making some sort of system that gives info about the bad guys automatically.
He finds out that probability of Batman finding some criminal is 609/625 in 20 days.
But they don’t have that much time. Bane has set a deadline of 5 days to blow off the city.
What are the chances that Batman will catch Bane in 5 days and save Gotham city?

Determine the test statistic (z* or t*) and the p-value for each of the following situations and Determine if they would cause the rejection of the null hypothesis if the confidence level was set at 95% in each case. (Hint: be wary of the sample size):
a) Ho: mu = 50 mL, Ha: mu "not equal to" 50 mL, sample mean = 47.3 mL, sample standard deviation= 5, n=20
b) Ho: mu "less than or equal to" 8.9 m^3, Ha: mu > 8.9 m^3, sample mean = 10 m^3, s = 3.5, n = 75
c) Ho: mu "greater than or equal to" 20^o C, Ha: mu < 20^o C , sample mean= 17.1^o C, s= 4.8^o C, n= 12
d) Ho: mu = 380 s, Ha: mu "not equal to" 380 s, sample mean = 400 s, s = 75, n = 40
e) Ho: mu = 48 units, Ha: mu "not equal to" 48 units, sample mean = 50 units, s = 9.5, n = 41

A biologist is studying the levels of arsenic that are naturally produced in some ground water sources. A mean level of 8.0 parts per billion (ppb) and less is considered safe for agricultural use. A random sample of 40 tests of the ground water at different locations in the town of Howick yields a sample mean of 8.4 ppb with a standard deviation of 1.7 ppb. Is there enough evidence to conclude that the arsenic levels are too dangerous to use for agricultural purposes at the 98% confidence level? Conduct a complete hypothesis test which includes
a) The null and alternative hypotheses, Ho and Ha
b) The critical value (confidence coefficient)
c) The test statistic (including sample mean and standard deviation)
d) The p-value
e) A decision (do or do not accept the null hypothesis)
f) A conclusion (that refers back to the question that was posed)

The Canadian Association of Pumpkin Growers is conducting a study to determine the pricing of their crops for the current season. Based on studies conducted in various regions across the country, the average cost of pumpkins for consumers is $3.18 per kg.

From a random sample of 15 farmer’s markets in the Montreal?area you determine that the average price for pumpkins is $4.52 per kg with a standard deviation of $2.20 per kg.

d) Construct a 98% confidence interval for the average price of pumpkins in the Montreal-area if the statistics remained unchanged despite the fact that 20 more pumpkins were added to the original sample and determine if it differs significantly from that of the rest of the country.
e) Construct a 95% confidence interval for the average price of pumpkins in the Montreal-area if a new sample of 15 pumpkins yields a sample mean of $4.52 per kg. and a standard deviation of $2.50 per kg. Determine if it differs significantly from that of the rest of the country.

TubeView, a digital television distribution company based in Gatineau (QC), hires a marketing firm to gauge the satisfaction levels of their customers. The CEO of TubeView has claimed that past polls have suggested that the customer satisfaction level is at 90%.
If this claim was true, what is the probability that in a random sample of 12 customers:
a) Exactly 8 customers are satisfied with TubeView’s service?
b) At least 10 customers are satisfied with TubeView’s service?
c) All of the customers they contact are satisfied with TubeView’s service?
d) At most 2 customers are not satisfied with TubeView’s service?
e) P(5 less than or equal to X < 8) where X = satisfied customer?