## 48. Reading Rates The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standar

Question

48. Reading Rates 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) What is the reading speed of a sixth-grader whose reading speed is at the 90th percentile

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1 week 2021-09-13T00:45:47+00:00 2 Answers 0

Step-by-step explanation:

Since the the reading speed of sixth-grade students is approximately normal, we would apply the formula for normal distribution which is expressed as

z = (x – µ)/σ

Where

µ = mean speed

σ = standard deviation

From the information given,

µ = 125 words per minute

σ = 24 words per minute

Looking at the normal distribution table, the z value corresponding to the 90th percentile(0.9), is 1.285

Therefore,

1.285 = (x – 125)/24

24 × 1.285 = x – 125

30.84 = x – 125

x = 125 + 30.84

x = 155.84

The reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.72 words per minute.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that: