Question

# 1. The weights of a certain brand of candies are normally distributed with a mean weight...

1. The weights of a certain brand of candies are normally distributed with a mean weight of 0.8542 g and a standard deviation of 0.0521 g. A sample of these candies came from a package containing 454 ​candies, and the package label stated that the net weight is 387.3 g.​ (If every package has 454 ​candies, the mean weight of the candies must exceed  387.3 Over 454= 0.8531 g for the net contents to weigh at least 387.3 ​g.) a. If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8531 g. The probability is...​(Round to four decimal places as​ needed.)

2. 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 139 lb and a standard deviation of 33.8 lb. 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.)

3. A boat capsized and sank in a lake. Based on an assumption of a mean weight of 139 ​lb, the boat was rated to carry 70 passengers​ (so the load limit was 9,730 lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 139 lb to 170 lb. Complete parts a and b below. Assume that a similar boat is loaded with 70 ​passengers, and assume that the weights of people are normally distributed with a mean of 174.2 lb and a standard deviation of 35.5 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 139 lb. The probability is.. ​(Round to four decimal places as​ needed.)

4. An airliner carries 150 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts​ (a) through​ (d).

a. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.

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

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