Answer:
62.416 inches.
Step-by-step explanation:
Given :Heights for group of people normally distributed with mean = 66 inches and standard deviation = 2.8 inches.
To Find: Find the height, h such that about 10% of people in the group are shorter than that height.
Solution:
Mean= [tex]\mu = 66[/tex]
Standard deviation = [tex]\sigma = 2.8[/tex]
We are given that Find the height, h such that about 10% of people in the group are shorter than that height.
So, p - value = 0.1
So using z table find z corresponding to this p value
So, z = -1.28
Now we are supposed to find the height such that about 10% of people in the group are shorter than that height.
So, we will use z score formula :
[tex]z =\frac{x-\mu}{\sigma}[/tex]
[tex]-1.28 =\frac{x-66}{2.8}[/tex]
[tex]-1.28 \times 2.8 =x-66[/tex]
[tex]-3.584 =x-66[/tex]
[tex]-3.584+66=x[/tex]
[tex]62.416=x[/tex]
Hence he height, h such that about 10% of people in the group are shorter than that height is 62.416 inches.
