Question

Assume women’s heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. a. If one woman is randomly selected, find the probability that her height is less than 64 inches. b. If 25 women are randomly selected, find the probability that they have a mean height less than 64 inches.

Answer 1

Answer:  a)  0.5636       b) 0.7881

Step-by-step explanation:

We assume that women’s heights are normally distributed .

Let x be the random variable that represents the shoe sizes.

Also, The population mean = $\mu=\text{63.6 inches}$ ; Standard deviation: $\sigma=\text{2.5 inches}$

a) Formula for z:-

$z=\dfrac{x-\mu}{\sigma}$

Put x= 64, we get

$z=\dfrac{64-63.6}{2.5}=0.16$

Now, the probability that the male shoe sizes are greater than 8 :-

$P(z$

Hence, the probability that her height is less than 64 inches = 0.5636

b. Sample size : n= 25

Then , the formula for z :-

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

Put x= 64, we get

$z=\dfrac{64-63.6}{\dfrac{2.5}{\sqrt{25}}}=0.8$

Then, the probability that they have a mean height less than 64 inches.:_

$P(z$

Hence, the probability that they have a mean height less than 64 inches. =0.7881

Answer 2

Answer:

0.0250 just got it right

Step-by-step explanation: