Please help me solve this in order for me to understand!

Question

In a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation of 5.5 days. Thirty-four percent of gestation periods are longer than how many days, rounded to the nearest whole number?

.

280 days

282 days

286 days

288 days

Answer 1

We know that whatever number of days (x) we pick it should result in a probability of .34. When we look at the z score table the z value that corresponds to .34 is about -.42. So we set -.42 = (x-m)/standard deviation.

==> -.42 = (x-284)/5.5. Solving for x gives us about 281.69 so about 282 days.