Question

1. I recently asked 100 middle school students to complete a statistics test. The mean score on the test was 30 points with a standard deviation of 5 points. The scores followed a normal distribution. Using this information, calculate the following:

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

P (score < 45 points) =

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

P(score > 30) =

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

P (25 points < score < 45 points) =

d. I want to know the cutoff value for the upper 10%. What score separates the lower 90% of scores from the upper 10%?

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

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

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

f. I would also like to know the cut off values for the highest 25%.

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

Answer 1

Answer:

Given that;

I recently asked 100 middle school students to complete a statistics test. The mean score on the test was 30 points with a standard deviation of 5 points.

a) What is the probability a student earned a score of 45 points or less?

45 - 30 P(score < 45 points) = P(Z <

P(score < 45 points) = P(Z <=

P(score < 45 points) = P(Z <3)

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

$P(score > 30) = P(Z>\frac{30-30}{5})$

$P(score > 30) = P(Z>\frac{0}{5})$

c) What is the probability a student earned a score between 25 and 45 points?

$P (25\, points < score < 45 \, points) =P(\frac{25-30}{5}<Z<\frac{45-30}{5})$

$P (25\, points < score < 45 \, points) =P(\frac{-5}{5}<Z<\frac{15}{5})$

d) I want to know the cutoff value for the upper 10%. What score separates the lower 90% of scores from the upper 10%?

Score = $\mu +2\sigma =30+1.282*5= 36.41$

e) I want to know the cutoff values for the lowest 25%.

Score = $\mu -2\sigma =30-0.674*5= 26.62$

f) I would also like to know the cut off values for the highest 25%.

Score = $\mu +2\sigma =30+0.674*5= 33.37$