What are the answers to these questions?

Question

According to a study in a journal of Human Reproduction, the length of human pregnancy has an average(mean) of 285 days with a standard deviation of 13 days. Assuming that the length of human pregnancy is normally distributed. Find the following:

a) The proportion of pregnancies whose length will be less than 259 days.

b) The probability that the length of pregnancy will be above 295 days.

c) The proportion of pregnancies whose length will be between 268 and 288 days.

d) The probability that the length of pregnancy is less than 252 or greater than 300

days.

e) How many births occur at the 30th percentile.

f) The probability that a pregnancy is no more than 210 days.

g) Are pregnancies that last more than 42 weeks rare? Explain your answer.

Answer 1

mean 285 SD = 13

x = days of pregnancy

a) P(x < 259) = P(z < (259 - 285)/13))

b) P(x > 295) = 1 - P(z < (295 - 285)/13))

c) P(268 < x < 288) = P( (268 - 285)/13 < z < (288 - 285)/13)

d) P(x > 300) or (x < 252) = (z > (300 - 295)/13) + {z > (252 - 285)/13)

e) 30th percentile, z = -0.52

-0.52 = (x - 285)/13, solve for x

f) 42 weeks = 294 days. P(x > 294) = P(z > (294 - 285)/13). If that probability is < 0.05, then it is rare.