Question

According to the U.S. Department of Education, 1,026,000 high school seniors (rounded to the nearest thousand) took the ACT test as part of the college admissions process. The mean composite score was 21.1 with a standard deviation of 4.8. The ACT composite score ranges from 1 to 36, with higher scores indicating greater achievement in high school. An admissions officer wants to find what percentage of samples of 50 students will have a mean ACT score less than 19.6. What numbers from the information above will the admissions officer need?

Answer 1

Z- score is - 2.21

Explanation:

Given that,

Mean
`(\mu)` = 21.1

Standard deviation
`(\sigma)` = 4.8

sample size (n) = 50

sample mean
`(\bar x)` = 19.6

we want to find, z-score corresponding to mean of 19.6

`Z = (x-\mu)/((\sigma)/(√(n)))`

`Z = (19.6-21.1)/( (4.8)/(√(50)))`

Z = =-2.21

Z-score is -2.21