Question

A study indicates that the weights of adults are normally distributed with a mean of 140 lbs and a standard deviation of 25 lbs.

a. What is the probability that a randomly selected adult weights between 120 and 165 lbs?

b. if 200 adults are randomly selected from this population, approximately how many of them weigh more than 170 lbs?

c. Find the value of weight X such that only 20% of adults weight less than that.

Answer 1

Solution :

Given that ,

mean = = 140

standard deviation = = 25

(a)

P(120 < x < 165) = P[(120 - 140)/ 25) < (x - ) /  < (165 - 140) / 25) ]

= (0.8 < z < 1)

= P(z < 1) - P(z < -0.8)

= 0.8413 - 0.2119

= 0.6294

(b)

P(x > 170) = 1 - P(x < 170)

= 1 - P[(x - ) / < (170 - 140) / 25]

= 1 - P(z < 1.2)

=0.1151

0.1151 * 200 = 23

23 of them weigh more than 170 lbs .

(c)

P(Z < -0.84) = 0.20

z = -0.84

Using z-score formula,

x = z * +

x = -0.84 * 25 + 140 = 119

Weight = 119