Question

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.

Required:
a. How short are the shortest 2.5% of all pregnancies?
b. Between what values do the lengths of the middle 95% of all pregnancies fall?
c. How long do the longest 2.5% of pregnancies last?

Answer 1

Kindly check explanation

Explanation:

Given that :

Mean (m) = 266 days

Standard deviation (s) = 16 days

A.) p(( Z ≤ (x - m) /s) = 2.5%

p(( Z ≤ (x - 266) /16) = 0.025

(x - 266) /16 = - 1.96 (Z probability calculator)

x - 266 = - 31.36

x = - 31.36 + 266

x = 234.64

B.)

p(( Z ≤ (x - m) /s) = 2.5%

p(( Z ≤ (x - 266) /16) = 0.025

(x - 266) /16 = - 1.96 (Z probability calculator)

x - 266 = - 31.36

x = - 31.36 + 266

x = 234.64

p(( Z ≤ (x - m) /s) = 2.5%

p(( Z ≤ (x - 266) /16) = 0.025

(x - 266) /16 = 1.96 (Z probability calculator)

x - 266 = 31.36

x = 31.36 + 266

x = 297.36

Hence,

234.64 < x <297.36

C.)

p(( Z ≤ (x - m) /s) = 2.5%

p(( Z ≤ (x - 266) /16) = 0.025

(x - 266) /16 = 1.96 (Z probability calculator)

x - 266 = 31.36

x = 31.36 + 266

x = 297.36