Question

The Ministry of Education estimates that the SAT scores of students in United States are normally distributed with mean 550 and standard deviation of 30.

a) Find the threshold value of SAT score where 10% of all students are above it.

b) Suppose that a sample of 60 students is randomly selected from United States population, and the sample is normally distributed, what is the probability that the mean SAT score of the sample of students is above 553?

Answer 1

Mean = = 550

Standard deviation = = 30

a) We have given P(X > x) = 0.10

z value 0.10 is 1.28

We have to find the value of x

b)

Sample size = n = 60

We have to find P( > 553)

For finding this probability we have to find z score.

That is we have to find P(Z > 0.77)

P(Z > 0.77) = 1 - P(Z < 0.77) = 1 - 0.7794 = 0.2206