Question

A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 173 lb and a standard deviation or 35 lb. You need to design an elevator that will safely carry 20 people. Assuming a worst case scenario of 20 male passengers, find the maximum total allowable weight if we want to a 0.99 probability that this maximum will not be exceeded when 20 males are randomly selected.
maximum weight =
Enter your answer rounded to the nearest whole number. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

CNNBC recently reported that the mean annual cost of auto insurance is 974 dollars. Assume the standard deviation is 257 dollars. You take a simple random sample of 64 auto insurance policies.
Find the probability that a single randomly selected value exceeds 967 dollars.
P(X > 967) =
Find the probability that a sample of size n=64 is randomly selected with a mean that exceeds 967 dollars.
P(M > 967) =
Enter your answers as numbers accurate to 4 decimal places.

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 122000 dollars. Assume the standard deviation is 31000 dollars. Suppose you take a simple random sample of 61 graduates.
Find the probability that a single randomly selected salary is at least 117000 dollars.
P(X > 117000) =
Find the probability that a sample of size n=61 is randomly selected with a mean that is at least 117000 dollars.
P(M > 117000) =
Enter your answers as numbers accurate to 4 decimal places.

Answer 1