Question

suppose the lengths of the pregnancies' of a certain animal are approx. normally distributed with a mean = 255 days and standard deviation of 14 days

what is the probability that a random sample of 48 pregnancies has a mean gestation of 250 days or less?

(d) the probability that the mean of a random sample of 48 pregnancies is less than 250 days is approx. ___?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 255

standard deviation = $\sigma$ = 14

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 14 / $\sqrt$ 48 = 2.0207

P($\bar x$$\leq$ 250) = P(($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$}$\leq$(250 - 255) / 2.0207)

= P(z $\leq$ -2.47)

= 0.9932

Probability = 0.9932

(d)

P($\bar x$ < 250) = P(($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (250 - 255) / 2.0207)

= P(z < -2.47)

= 0.9932

The probability that the mean of a random sample of 48 pregnancies is less than 250 days is approx.0.9932