Question

I asked 100 students to complete a statistics test. the mean score on the test was 30 points with a standard deviation of 5 points. using this information and the normal distribution, calculate the following: [want to check my overall answers and help with the process of some] thank you

a. what is the probability a student earned a score of 45 points or less?

P(score <45 points)

i got 0.9987

b. what is the probability a student earned a score higher than 30 points?

P(score > 30 points)

not sure how to do this one

c. what is the probability a student earned a score between 25 and 45 points?

P(25 points < score < 45 points)

overall got 0.84.

d. i want to know the cutoff value for the upper 10%. what score separated the lower 90% of scores from the upper 10%?

P(score<____)=90% or 0.90 cumulative area to the left.

[i got p(score<0.8159)=90% --> x=34.0795 separates the scores.

e. want to know the cutoff values for the lowest 25% and the highest 25%

[not sure how to do these]

P(score<____)=25% or 0.25 cumulative area to the left.

P(score>____)=25% or 0.25 cumulative area to the right

Answer 1

Here we have

(a)

The z-score for x= 45 is

The probability a student earned a score of 45 points or less is

Answer: 0.9987

(b)

The z-score for x= 30 is

The probability a student earned a score higher than 30 is

Answer: 0.50

(c)

The z-score for x= 25 is

The z-score for x= 45 is

The required probability is

Answer: 0.8400

(d)

We need z-score than t has 0.90 area to its left. The z-score 1.28 has 0.90 area to its left. So,

Answer: 36.4

(e)

We need z-score than t has 0.25 area to its left. The z-score -0.67 has 0.25 area to its left. So,

The cutoff values for the lowest 25% is 26.65.

We need z-score than t has 0.75 area to its left. The z-score 0.67 has 0.75 area to its left. So,

The cutoff values for the highest 25% is 33.35.