Question

the gestation time for cows is normally distributed with a mean of 284 days and a standard deviation of 12 days. at a local Ranch over the course of a year they're 820 calf births. of these how many would be expected to have a gestation time of less than 270 days​

Answer 1

Answer:

100 calfs

Step-by-step explanation:

We must calculate the probability that the cows have a gestation time of less than 270 days. If X represents the gestation time of a randomly selected cow, then we look for:

$P (X <270)$

Acora we calculate the Z-score

$Z=\frac{X-\mu}{\sigma}$

In this case

$\mu=284\ days\\\\\sigma = 12\ days$

So

$P (X <270) =P (\frac{X-\mu}{\sigma} <\frac{270-284}{12})=P(Z<-1.167)$

Looking in the normal standard table we have to

$P(Z<-1.167)=0.1216$

Finally, the expected number of calf "E" that will have a gestation time of less than 270 days is:

$E=820*P (X <270)\\\\E=820*0.1216$

E=99.71≈100 Calfs