Question

The average human gestation period is 270 days with a standard deviation of 9 days. The period is normally distributed. What is the probability that a randomly selected woman's gestation period will be between 261 and 279 days? Find the nearest answer.

Answer 1

Probability that a randomly selected woman's gestation period will be between 261 and 279 days is 0.68.

Explanation:

We are given that the average human gestation period is 270 days with a standard deviation of 9 days. The period is normally distributed.

Firstly, Let X = women's gestation period

The z score probability distribution for is given by;

Z =
`( X - \mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = average gestation period = 270 days

`\sigma` = standard deviation = 9 days

Probability that a randomly selected woman's gestation period will be between 261 and 279 days is given by = P(261 < X < 279) = P(X < 279) - P(X
`\leq` 261)

P(X < 279) = P(
`( X - \mu)/(\sigma)` <
`(279-270)/(9)` ) = P(Z < 1) = 0.84134

P(X
`\leq` 261) = P(
`( X - \mu)/(\sigma)`
`\leq`
`(261-270)/(9)` ) = P(Z
`\leq` -1) = 1 - P(Z < 1)

= 1 - 0.84134 = 0.15866

Therefore, P(261 < X < 279) = 0.84134 - 0.15866 = 0.68

Hence, probability that a randomly selected woman's gestation period will be between 261 and 279 days is 0.68.