Answer :
Answer:
Probability that the student scored between 455 and 573 on the exam is 0.38292.
Step-by-step explanation:
We are given that Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118.
Let X = Math scores on the SAT exam
So, X ~ Normal([tex]\mu=514,\sigma^{2} =118^{2}[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean score = 514
[tex]\sigma[/tex] = standard deviation = 118
Now, the probability that the student scored between 455 and 573 on the exam is given by = P(455 < X < 573)
P(455 < X < 573) = P(X < 573) - P(X [tex]\leq[/tex] 455)
P(X < 573) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{573-514}{118}[/tex] ) = P(Z < 0.50) = 0.69146
P(X [tex]\leq[/tex] 2.9) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{455-514}{118}[/tex] ) = P(Z [tex]\leq[/tex] -0.50) = 1 - P(Z < 0.50)
= 1 - 0.69146 = 0.30854
The above probability is calculated by looking at the value of x = 0.50 in the z table which has an area of 0.69146.
Therefore, P(455 < X < 573) = 0.69146 - 0.30854 = 0.38292
Hence, probability that the student scored between 455 and 573 on the exam is 0.38292.