The reading speed of sixth-grade students is approximately normal, with a mean s

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 probabliltiy that a randomly selected sixth-grade student reads more than 140 words per minute. (D) find and interpret the probablility that a randomly selected sixth-grade student reads between 110 and 130 words per minute. (E)would it be unusual for a sixth grader to read more than 200 words per minute? why?

Explanation / Answer

a)
std. dev. = 24
Variance = 24^2 = 576
Normal model = N(125, 576)

b)
P(X < 100)
= P(z < (100 - 125)/24))
= P(z < -1.0417)
= 0.148783124

c)
P(X > 140)
= P(z > (140 - 125)/24))
= P(z > 0.625)
= 0.265985529

d)
P(110 < X < 130)
= P((110 - 125)/24 < z < (130 - 125)/24)
= P(-0.625 < z < 0.2083)
= 0.316530118

e)
P(X > 200)
= P(z > (200 - 125)/24))
= P(z > 3.125)
= 0.000889025

As probability of this is very less, we can say that this is unusual.

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