HW #13 - Homework-12,13 61 Assume that the heights of adult...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework-12,13 61. Assume that the heights of adult males residing in the US (’males’ for short) are approximately normally distributed with mean 69.0 inches and standard deviation 2.8 inches. a. Find the proportion of males whose heights lie between 65.5 inches and 74.6 inches. b. If a male’s height is 0.4 standard deviations below the mean, how tall is he and what is the probability that a male, chosen at random, is within two inches of his height? c. In a random sample of 6 males, what is the probability that exactly 2 of them will be over six feet tall? SOLUTION: Let X indicate the height of randomly selected adult male residing in the US, i.e. X N(69 , 2 . 8 2 ) a. P(65 . 5 X 74 . 6) = P( 65 . 5 69 2 . 8 Z 74 . 6 69 2 . 8 ) =P(Z 2) P(Z ≤− 1 . 25) = 0 . 9772 0 . 1056 = 0 . 8716. b. Height=69-(0.4)(2.8)=67.88. P(67 . 88 2 X 67 . 88 + 2) = P( 65 . 88 69 2 . 8 Z 69 . 88 69 2 . 8 ) 0 . 31) P(Z 1 . 11) = 0 . 6217 0 . 1335 = 0 . 4882. c. Let Y indicate the number of males taller than 6 feet in the sample (of size 6). Y Bin(6 ,p ) where p =P(X > 6(12)) = P(Z > 72 69 2 . 8 )=1 P(Z 1 . 07) = 1 0 . 8577 = 0 . 1423. P(Y = 2) = ° 6 2 ± (0 . 1423) 1 (1 0 . 1423) 6 1 =0 . 164 62. Assume that the apparatus for filling containers of product X is calibrated in such a way
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

HW #13 - Homework-12,13 61 Assume that the heights of adult...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online