Question

1/ The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 530 and a standard deviation of 160. If a college requires a student to be in the top 35 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?
answer:(round to the nearest integer

2/ A random sample of 1300 registered voters in Flagstaff found 819 registered voters who support immigration reform. Find a 95% confidence interval for the true percent of registered voters in Flagstaff who support immigration reform. Express your results to the nearest hundredth of a percent. .

Answer:  to  %

Answer 1

Solution :

1) Let X be a random variable which represents the combined math and verbal scores for students taking a national standardized examination for college admission.

Given that,

Mean (μ) = 530

SD (σ) = 160

Let the minimum score required to be in top 35% is k.

Hence, P(X > k) = 0.35

We know that, if X ~ N(μ, σ²) then

..................(1)

Using "qnorm" function of R we get, P(Z > 0.3853) = 0.35

Comparing, P(Z > 0.3853) = 0.35 and (1) we get,

On rounding to nearest integer we get,

k = 592

Hence, the minimum score that a student can obtain and still qualify for admission at the college is 592.