Using the Central Limit Theorem assignment

The number of miles that regular tires last has a Normal distribution with a mean of 50,000 miles and a standard deviation of 8,200 miles. If a random sample of 4 tires are selected, what is the probability that the mean number of miles they last is more than 60,000 miles? Use this standard Normal table to calculate this probability.

0.0075

For which situations would it be appropriate to calculate a probability about the difference in sample means?

Both population shapes are unknown. n1 = 50 and n2 = 100. Population 1 is skewed right and population 2 is approximately Normal. n1 = 50 and n2 = 10 Both populations have unknown shapes. n1 = 50 and n2 = 100.

The number of miles that regular tires last has a Normal distribution with a mean of 50,000 miles and a standard deviation of 8,200 miles. A competitor creates a new brand of tire, SuperWear Tires. The number of miles that SuperWear lasts has a Normal distribution with a mean of 75,000 miles and a standard deviation of 15,500 miles. If a random sample of 16 regular tires is selected and a random sample of 25 SuperWear tires is selected, what is the probability that the sample mean number of miles of SuperWear is greater than the sample mean number of miles obtained by the regular tires? Use this standard Normal table to calculate this probability.

approximately 1

Students at Edgewood High School spend a lot of time studying. The distribution of study time is skewed to the left with a mean of 3.5 hours per day and a standard deviation of 1.25 hours per day. A statistics student would like to select a sample from this population and calculate the probability that the sample mean study time exceeds 4 hours. For which sample size would it be appropriate for the student to calculate the desired probability?

n = 40

The annual cost of diapers for families that have one or more children under the age of 4 is skewed to the right with a mean of $1,225 and a standard deviation of $633. If a random sample of 15 families that have one or more children under the age of 4 are selected, what is the probability that their mean annual diaper cost is more than $1,500? Is it appropriate to calculate this probability?

no not appropriate

A company manufactures and sells bulk orders of pencils and pens. The amount of profit that they make per customer order is skewed to the right for both items. The mean profit per pencil order is $575 with a standard deviation of $57. The mean profit per pen order is $615 with a standard deviation of $75. If a random sample of 40 pencil orders and a random sample of 50 pen orders are selected, what is the probability that the sample mean profit from the pencil order is greater than the sample mean profit from the pen order? Is it appropriate to calculate this probability?

yes 0.002

The annual cost of diapers for families that have one or more children under the age of 4 is skewed to the right with a mean of $1,225 and a standard deviation of $633. If a random sample of 35 families that have one or more children under the age of 4 are selected, what is the probability that their mean annual diaper cost is more than $1,500?

yes 0.005

The number of miles that regular tires last has a Normal distribution with a mean of 50,000 miles and a standard deviation of 8,200 miles. A competitor creates a new brand of tire, SuperWear Tires. The number of miles that SuperWear lasts has a Normal distribution with a mean of 75,000 miles and a standard deviation of 15,500 miles. If a random sample of 16 regular tires is selected and a random sample of 25 SuperWear tires is selected, the probability that the sample mean number of miles of SuperWear is greater than the sample mean number of miles obtained by the regular tires is approximately 1. Is there convincing evidence that the true mean number of miles obtained by SuperWear tires is greater than that of the regular tires?

yes likely greater than

The number of miles that regular tires last has a Normal distribution with a mean of 50,000 miles and a standard deviation of 8,200 miles. If a random sample of 4 tires are selected, the probability that the mean number of miles they last is more than 60,000 miles is 0.0075.

yes unlikely