Respuesta :
Answer:
Jenny performed better in statistic test as compared to history exam.
Step-by-step 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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(AP statistic score of 95)
P(x < 95)
[tex]P( x < 95) = P( z < \displaystyle\frac{95 - 84}{4.5}) = P(z < 2.445)[/tex]
Calculation the value from standard normal z table, we have, Â
[tex]P(x < 95) =0.993 = 99.3\%[/tex]
P(AP U.S. History of 90)
P(x < 90)
[tex]P( x < 90) = P( z < \displaystyle\frac{90 - 75}{8.2}) = P(z < 1.829)[/tex]
Calculation the value from standard normal z table, we have, Â
[tex]P(x < 95) =0.966 = 96.6\%[/tex]
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%.
