Question

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

217.502 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 0.0591.

​(Round to four decimal places as​ needed.)

b. The probability is ..........

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.)

Answer 1

X :overhead reach distances of adult females

X~ N(205,8)

a).the probability that an individual distance is greater than 217.50 cm be:-

[ in any blank cell of excel type =NORMSDIST(1.5625) press enter]

b)sample size(n) =20

the probability that the mean for 20 randomly selected distances is greater than 203.50 cm be:-

[ in any blank cell of excel type =NORMSDIST(0.8385) press enter]

c).we need to think about the sample size in a sampling distribution :-

i).when the shape of the distribution of population is not known to us

ii).the the population is not normally distributed.

here, it is stated in question that the population is normally distributed so,normal distribution can be used in part​ (b), even though the sample size does not exceed​ 30.

2)X : weight of pilots.

X ~ N(135,30.1)

the probability that his weight is between 130 lb and 171 lb be:-

[ in any blank cell of excel type =NORMSDIST(1.196) press enter]

[ in any blank cell of excel type =NORMSDIST(-0.1661) press enter]

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