Question

round to 4 decimal places as needed pls

This Question: 1 pt 20 of 24 ( complete This Test: 24 pts possible Suppose that an alline uses a seat with of 16.7 in. Assume men have Hip breadths that are normally distributed with a moan of 14.4 in, and a standard deviation of 1 in Complete parts (a) through (c) below. (a) Find the probability that if an individual man is randomly selected, his hip breadh will be greater than 16.7 in. The probability is (Round to four decimal places as needed) (b) a plane is filled with 117 randomly selected men, find the probability that these men have a mean hip breadth greater than 16.7 in. The probabilty is (Round to four decimal places as needed.) (e) Which result should be considered for any changes in seat design: the result from part (n) or part (b)? The result from should be considered because the seats are occupied by Individuais rather than means. only average individuals should be considered Enter your answer in each of the answer boxes

Answer 1

Let X be the R.V that denotes the distribution of hip-breadth. Then X follows Norm(14.4,1)

Then by standardizing,

Then Z follows a standard normal distribution. Now by using the standard normal tables,

Mean	14.4
Standard Deviation	1
Probability for X > 16.7
X Value	16.7
Z Value	2.3
P(X>16.7)	0.0107

Hence P(X>16.7) = 0.0107

b)

Now we have a sample of 117 passengers and by CLT s,

$\bar{X}\rightarrow N(\mu,\frac{\sigma}{\sqrt{n}})$

And standardizing this, we have

Mean	14.4
Standard Deviation	0.09245
Probability for X_bar > 16.7
X Value	16.7
Z Value	24.878304
P(X_bar >16.7)	~0

Hence, P(X_bar > 16.7) is approximately zero.

c)

The result from B should be considered because only average individuals should be considered.