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.

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 = ~ N(0,1)

where, = average gestation period = 270 days

             = 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 261)

         P(X < 279) = P( < ) = P(Z < 1) = 0.84134

         P(X 261) = P( ) = P(Z -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.

answer

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