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

Answer:

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

Step-by-step 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 = $\frac{ X - \mu}{\sigma}$ ~ 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( $\frac{ X - \mu}{\sigma}$ < $\frac{279-270}{9}$ ) = P(Z < 1) = 0.84134

         P(X $\leq$ 261) = P( $\frac{ X - \mu}{\sigma}$ $\leq$ $\frac{261-270}{9}$ ) = 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.