Question

3.67 The mean weight of a large group of people is 180 lb and the standard deviation is 15 lb. If the weights are normally distributed, find the probability that a person picked at random from the group will weigh (a) between 160 and 180lb, (b) above 200 lb, (c) below 150 lb. Ans. (a) 0.4082, or 40.82% (b) 0.0918 (c) 0.228

Please show how the answers were calculated.

Answer 1

Here we have Mean = $\mu$ = 180, Standard deviation = $\sigma$ = 15

Let x denotes weight of a large group of people. The weights are normally distributed.

a) We need to find, probability between 160 and 180 lb.

p ( 160 < x < 180 )

------------( converted in to z score )

15 ( 031 – ost? 1-2 083097) - =

= p ( -1.33 < z < 0 )

= p ( z < 0 ) - p ( z < -1.33 )

= 0.5 - 0.0918 -----------------( using excel formula "=norm.s.dist(0,1)" and "=norm.s.dist(-1.33,1)" )

= 0.4082

b) We need to find, probability above 200 lb.

p ( x > 200 )

= 1- p ( x $\leq$ 200 )

--------- ( converted in to z score )

=1-1 (0-4-200=180) 15

= 1 - p ( z $\leq$ 1.33 )

= 1 - 0.9082 --------------( using excel formula " =norm.s.dist(1.33,1)" )

= 0.0918

c) We need to find, probability below 150.

p ( x < 150 )

------------- ( converted in to z score )

15 (051--ost –z)(=

= p ( z < -2 )

= 0.0228 --------------( using excel formula " =norm.s.dist(-2.1)" )