For a normal distribution given a standard deviation of 3.8 in a mean of 54 what percent lies above 48

A 0.1690

B 0.0571

C 0.7660

D 0.9429

choice D.) 0.9429

Step-by-step explanation:

Given a Normal data set

mean u = 54

standard deviation s = 3.8

we want P (X > 48)

Standardize this probability so we can use Z-scores.

P (X > 48) = P ((X - u) / s > (48 - 54) / 3.8) = P (Z > - 1.5789)

so I look for P (Z > 1.5789) = 0.0571

so P (Z > - 1.5789) = 1 - P (Z > 1.5789) = 1 - 0.0571 = 0.9429