Question

The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. (a) Draw a normal model that describes the reading speed of sixth-grade students. (b) Find and interpret the probability that a randomly selected sixth-grade student reads less than 100 words per minute. (c) Find and interpret the probability that a randomly selected sixth-grade student reads more than 140 words per minute.

Answer 1

Answer:

Part A

μ of the reading speed of sixth-grade students = 125 words

σ of the reading speed of sixth-grade students = 24 words

Part B

The probability that a randomly selected sixth-grade student reads less than 100 words per minute is 14.92%

Part C

The probability that a randomly selected sixth-grade student reads more than 140 words per minute is 26.43%

Step-by-step explanation:

Part A:

μ of the reading speed of sixth-grade students = 125 words

σ of the reading speed of sixth-grade students = 24 words

Part B:

1. Let's find the z-score for a randomly selected sixth-grade student that reads less than 100 words per minute:

z-score = (100 - 125)/24

z-score = -25/24

z-score = -1.04

2. Now, let's find out the probability that a randomly selected sixth-grade student that reads less than 100 words per minute, using the z-table:

P (-1.04) = 0.1492

This means that the probability that a randomly selected sixth-grade student that reads less than 100 words per minute is 14.92%

Part C.

1. Let's find the z-score for a randomly selected sixth-grade student that reads more than 140 words per minute:

z-score = (140 - 125)/24

z-score = 15/24

z-score = 0.63

2. Now, let's find out the probability that a randomly selected sixth-grade student that reads more than 140 words per minute, using the z-table:

P (0.63) = 0.7357

But we're being asked for a randomly selected student that reads more than 140 words, then:

1 - P(0.63) = 1 - 0.7357 = 0.2643

This means that the probability that a randomly selected sixth-grade student that reads more than 140 words per minute is 26.43%