Question

I need solution thank you!

2. The heights for 5 year boys are normally distributed with a mean height of 43 inches and a standard deviation of 5.3 inches. A sample of 60 boys is randomly selected. Find (a) (8 points) The probability that mean height of boys for the sample of 60 boys is between 41 inches and 45 inches. (b) (5 points) The height of a boy that corresponds to the 82th percentile.

you can use these tables and formulas.

Answer 1

Here, we have mean (u) = 43 Standard deviation (0)2 5.3 Sample size (n) = 60 (9) PL 415 X< 45 11 41-43 X-4 45-437 = P(-2.92 < 25 2.92) = P125 2.92) – P125-2.92) = 0.99825-0.00175 i from standard normal Bobability = 10.9965)

(b) 82 percentile PL x < nj = 0.82 * PlX-4 <2 Dlx-4 cx-43 1=0.82 olin 5.3160 ) > PL ZE X-43 ) = 0.82 0.6842) → - X- 43 0:6842 = 20.89= 0.9151 from standard nor mal tablet + x = 0.915*0.68 42 +43 = 43.626043 = 43.63] Round to 2 decimal 1 places The height of the boy that corresponds to the 82th percentile - [43.63