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?

Answer 1

286

Step-by-step explanation:

Given :

Mean (m) = 284

Standard deviation (s) = 5.5

P(Z > x) = 0.34

According to the standardized formula :

Zscore = (x - m) / s

Uaing the Z probability calculator ; The Z value at P(Z > x) = 0.34 is 0.412

Hence, Zscore = 0.412

Zscore = (x - m) / s

0.412 = (x - 284) / 5.5

5.5 * 0.412 = x - 284

2.266 = x - 284

x = 2.266 + 284

x = 286.266

x = 286 (nearest whole number)