Question

Length of human pregnancies follows a normal distribution with a population mean of 266 days and a standard deviation of 16 days.

A) 90% of pregnancies last between how many days?

B) 60% of pregnancies last between how many days?

Answer 1

Given that,

mean = = 266

standard deviation = = 16

middle 90% of score is

P(-z < Z < z) = 0.90

P(Z < z) - P(Z < -z) = 0.90

2 P(Z < z) - 1 = 0.90

2 P(Z < z) = 1 + 0.90 = 1.90

P(Z < z) = 1.90 / 2 = 0.95

P(Z <1.65 ) = 0.95

z  ±1.65

z =-1.65

Using z-score formula  

x= z * +

x= - 1.65*16+266

x= 239.6

x=240

z = 1.65

Using z-score formula  

x= z * +

x=165 *16+.266

x= 292.4

x=292

answer =240 day and 292 day

(B)

middle 60% of score is

P(-z < Z < z) = 0.60

P(Z < z) - P(Z < -z) = 0.60

2 P(Z < z) - 1 = 0.60

2 P(Z < z) = 1 + 0.60 = 1.60

P(Z < z) =1.60 / 2 = 0.80

P(Z <0.84) = 0.80

z  ±0.84

z= - 0.84

Using z-score formula  

x= z * +

x= - 0.84*16+266

x= 252.56

x=253

z = 0.84

Using z-score formula  

x= z * +

x=0.84 *16+266

x= 279.44

x=279

answer = 253 day and 279 day