Question

Jenny is taking AP Statistics and AP U.S. History. Jenny scored a 95 on an AP Statistics test where the mean score was 84 with a standard deviation of 4.5. She then scored a 90 on an AP U.S. History test with a mean score of 75 and a standard deviation of 8.2. On which test did Jenny perform better relative to others who have taken the test? Justify your answer.

Answer 1

Jenny performed better in statistic test as compared to history exam.

Explanation:

We are given the following information in the question:

AP Statistics

Mean, μ = 84

Standard Deviation, σ = 4.5

AP U.S. History

Mean, μ = 75

Standard Deviation, σ = 8.2

We are given that the distribution of scores are a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(AP statistic score of 95)

P(x < 95)

`P( x < 95) = P( z < \displaystyle(95 - 84)/(4.5)) = P(z < 2.445)`

Calculation the value from standard normal z table, we have,

`P(x < 95) =0.993 = 99.3\%`

P(AP U.S. History of 90)

P(x < 90)

`P( x < 90) = P( z < \displaystyle(90 - 75)/(8.2)) = P(z < 1.829)`

Calculation the value from standard normal z table, we have,

`P(x < 95) =0.966 = 96.6\%`

Jenny did better on AP statistics, because she scored better than 99.3% of the students on statistics exam that is her percentile is 99.3% as compared to 96.6% of the students on the history exam where her percentile is 96.6%.