Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 159 lb and a standard deviation of 34.3 lb lb. a. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 201 lb. The probability is approximately 0.4931. ​(Round to four decimal places as​ needed.) b. If 30 different pilots are randomly​ selected, find the probability that their mean weight is between 150 lb and 201 lb. The probability is approximately ___. ​(Round to four decimal places as​ needed.)

Answer 1

GIVEN:

The new population of pilots has normally distributed weights with a mean and a standard deviation .

PROBABILITY THAT WEIGHT OF SEAT IS BETWEEN 150lb AND 201lb :

To find the probability we should convert the raw score into standard score Z using the given formula,

The probability that weight of seat is between 150lb and 201lb is,

(Since )

Using z table, the first probability value is the value with corresponding row 1.2 and column 0.02 and the second probability value is the value with corresponding row -0.2 and column 0.06.

  

Thus the probability that weight of seat is between 150lb and 201lb is .

PROBABILITY THAT WEIGHT OF SEAT IS BETWEEN 150lb AND 201lb IF 30 PILOTS ARE RANDOMLY SELECTED: :

To find the probability we should convert the into standard score Z using the given formula,

The probability that weight of seat is between 150lb and 201lb if 30 pilots are randomly selected is,

(Since )

Using z table, the first probability value is the value with corresponding row 1.2 and column 0.02 and the second probability value is the value with corresponding row -0.2 and column 0.06.

  

Thus the probability that weight of seat is between 150lb and 201lb if 30 pilots are randomly selected is .