A manufacturer knows that their items have a normally distributed length, with a mean of 14.9 inches, and standard deviation of 3.1 inches.
A manufacturer knows that their items have a
If 13 items are chosen at random, what is the probability that their mean length is less than 13.6 inches?
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 178 lb and a standard deviation or 32 lb. You need to design an elevator that will safely carry 18 people. Assuming a worst case scenario of 18 male passengers, find the maximum total allowable weight if we want a 0.995 probability that this maximum will not be exceeded when 18 males are randomly selected.
maximum weight = -lb Round to the nearest pound.
Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.
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