Question

The distribution of number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and standard deviation 7. Volunteers in the top 20 percent of hours worked will
receive a certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the
number of hours the volunteer worked is less than 90?
A 0.077
B 0.123
C 0 0.618
D 0.618
E 0.923

Answer 1

Answer:

E 0.923

Step-by-step explanation:

The Z score is a measurement used in statistics to determine the relationship between a value and a mean of a group of values measured as standard deviation from the mean. The z score (z) is given as:

$z=\frac{x-\mu}{\sigma}$, Where μ is the mean, σ is the standard deviation and x is the value.

Given that:

σ = 7, μ = 80 and x = 90  

$z=\frac{x-\mu}{\sigma}=\frac{90-80}{7} =1.43$

From the normal distribution table, P(X < 90) = P(z < 1.43) = 0.923