Statistics and Probability Answers

A company that produces batteries claims that the life expectancy of their batteries is 90 hours with a standard deviation of 10 hours. A consumer interest group believes that the actual battery life expectancy of these batteries is shorter than the claimed battery life. In order to prove this, they test a random sample of 20 batteries which resulted a mean of 87 hours. Conduct a hypothesis test with a significance level of 0.05

A company that produces batteries claims that the life expectancy of their batteries is 90 hours with a standard deviation of 10 hours. A consumer interest group believes that the actual battery life expectancy of these batteries is shorter than the claimed battery life. In order to prove this, they test a random sample of 20 batteries which resulted a mean of 87 hours. Conduct a hypothesis test with a significance level of 0.05

For each day, independent of the others, the length of time for one individual to be servedat a cafeteria is a random variable having an exponential distribution with a mean of 4 minutes. What is the probability that a person is served in less than 3 minutes on at least 4 of the next 6 days?

A credit card company monitors cardholder transaction habits to detect any unusual activity. Suppose that the dollar value of unusual activity for a customer in a month follows a normal distribution with mean $250 and variance $391. a. What is the probability of $250 to $300 in unusual activity in a month? b. What is the probability of more than $300 in unusual activity in a month? c. Suppose that 10 customer accounts independently follow the same normal distribution. What is the probability that at least one of these customers exceeds $300 in unusual activity in a month? 

The life of a certain type of automobile tire is normally distributed with mean 34,000 miles and standard deviation 4000 miles. a. What is the probability that such a tire lasts over 40,000 miles? b. What is the probability that it lasts between 30,000 and 35,000 miles? c. Given that it has survived 30,000 miles, what is the conditional probability that it survives another 10,000 miles? 

 A hospital keeps records of its emergency-room traffic. Those records indicate that, beginning at 6:00 P.M. on any given day, the elapsed time until the first patient arrives has an exponential distribution with parameter λ = 6.9, where time is measured in hours. Determine the probability that, beginning at 6:00 P.M. on any given day, the first patient arrives

a. between 6:15 P.M. and 6:30 P.M.

b. before 7:00 P.M.

c. given that the first patient doesn’t arrive by 6:15 P.M., determine the probability that she arrives by 6:45 P.M.

Carl has completed 8 math homework assignments that are all worth 20 points, and his mean score is 17. Carlos has two more 20-point homework assignments to complete before his progress report gets sent out, and he wanted to raise his mean score to an 18. Is it possible for Carlos to raise his score to an 18?

 A bulb manufacturer claims that the lives of its bulbs are normally distributed with a mean of 6000 hours and a standard deviation of 400 hours. A random sample of 16 bulbs had an average life of 5850 hours. If the manufacturer’s claim is correct-

a. What is the sampling distribution of the sample mean?

b. what is the probability of finding a sample mean of 5850 or less?

Show complete solutions for each item. 

Locate the following percentile under the normal curve

Find the nearest area and the z-score.

Percentile 

a. 𝑃₇₆   

b. 𝑃₅₄   

c. 𝑃₃₄   

d. 𝑃₂₅   

e. 𝑃₉₄   

f. 𝑃₈₉   

g. 𝑃₉₀   

h. 𝑃₆₈   

i. 𝑃₁₅   

j. 𝑃₄₂   

It has been reported that 70% of university students do volunteer work during their summer vacation. Four students are randomly selected to do volunteer work.

a. The probability that at least 1 student will do volunteer work this summer (correct to 3 decimal places) is 

b. The probability that exactly 3 graduates will not do any volunteer work this summer (correct to 4 decimal places) is 

c. The expected number of students (correct to 1 decimal place) who will not do volunteer work this summer is