The overhead reach distances of adult females are normally distributed with a mean of 200 cm

200cm and a standard deviation of 7.8 cm

7.8cm.

a. Find the probability that an individual distance is greater than 209.30

209.30 cm.

b. Find the probability that the mean for 15

15 randomly selected distances is greater than 198.50 cm.

198.50cm.

c. Why can the normal distribution be used in part(b), even though the sample size does not exceed30?

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Assume that females have pulse rates that are normally distributed with a mean of mu equals 75.0

=75.0 beats per minute and a standard deviation of sigma equals 12.5

=12.5 beats per minute. Complete parts(a) through(c) below.

a. If 1 adult female is randomlyselected, find the probability that her pulse rate is between 71

71 beats per minute and 79

79 beats per minute.

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An elevator has a placard stating that the maximum capacity is 1264

1264 lblong dash

8

8 passengers.So, 8

8 adult male passengers can have a mean weight of up to 1264 divided by 8 equals 158 pounds.

1264/8=158pounds. If the elevator is loaded with 8

8 adult malepassengers, find the probability that it is overloaded because they have a mean weight greater than 158

158 lb.(Assume that weights of males are normally distributed with a mean of 165 lb

165lb and a standard deviation of 29 lb

29lb.) Does this elevator appear to besafe?

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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120

120 lb and 181

181 lb. The new population of pilots has normally distributed weights with a mean of 129 lb

129lb and a standard deviation of 32.2 lb

32.2lb.

a. If a pilot is randomlyselected, find the probability that his weight is between 120

120 lb and 181

181 lb.

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The acceptable level for insect filth in a certain food item is 2

2 insect fragments(larvae, eggs, bodyparts, and soon) per 10 grams. A simple random sample of 60

60 ten-gram portions of the food item is obtained and results in a sample mean of x overbar

xequals

=2.5

2.5 insect fragments perten-gram portion

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A simple random sample of size nequals

=46

46 is obtained from a population with mu

equals

=64

64 and sigma

equals

=14

14.

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the samplemean? Assuming that this condition istrue, describe the sampling distribution of x overbar

x.

(b) Assuming the normal model can beused, determine P(x overbar

xless than

<67.1

67.1).

(c) Assuming the normal model can beused, determine P(x overbar

xgreater than or equals

66.2

66.2).