Question

1. The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days.         
   1. What percent of pregnancies are due 253 to 283 days?
   2. Determine the percent of pregnancies with a duration less than 238 days.

Answer 1

Solution :

Given that ,

mean = = 268

standard deviation = = 15

P(253 < x < 283) = P((253 - 268) / 15) < (x - ) /  < (283 - 268) / 15) )

= P(-1 < z < 1)

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

= 0.8413 - 0.1587

= 0.6826

= 68.26%

Answer = 68.26%

(b)

P(x < 238) = P((x - ) / < (238 - 268) / 15)

= P(z < -2)

= 0.0228

= 2.28%

Answer = 2.28%