Question

1-4. The reading speed of second-grade students is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 12 wpm.

1. What is the z-score for a second-grade student who reads 100 wpm?

2. What is the probability a randomly selected second-grade student will read more than 100 wpm?

3. What is the reading speed of a second grader whose reading speed is at the 90th percentile?

Please Show all work!!

Answer 1

Solution :

1)

z = (x - ) / = (100 - 90) / 12 = 0.83

2)

P(x > 100) = 1 - P(x < 100)

= 1 - P[(x - ) / < (100 - 90) / 10]

= 1 - P(z < 0.83)

= 0.2033.

Probability = 0.2033

3)

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 12 + 90 = 105.36

90th percentile = 105.36