Question

1. The overhead reach distances of adult females are normally distributed with a mean of

205 cm and a standard deviation of 8 cm. a. Find the probability that an individual distance is greater than 217cm .502 cm 17.50 cm.

b. Find the probability that the mean for 20 randomly selected distances is greater than 203.50 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

a. The probability is ..... ​(Round to four decimal places as​ needed.)

2. An elevator has a placard stating that the maximum capacity is

1328 lb long—8 passengers.​ So, 8 adult male passengers can have a mean weight of up to 1328/8=166 pounds. If the elevator is loaded with 8

adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than

166 lb.​ (Assume that weights of males are normally distributed with a mean of 173 lb and a standard deviation of 34 lb​.)

Does this elevator appear to be​ safe?

The probability the elevator is overloaded is....  (Round to four decimal places as​ needed.)

3. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between

130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 135 lb

and a standard deviation of 30.1 lb a. If a pilot is randomly​ selected, find the probability that his weight is between 130

lb and 171 lb.The probability is approximately .... ​(Round to four decimal places as​ needed.)

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