Question

What is the probability that a random sample of second grade students from the city results in a mean reading rate of more than words per minute?

1. The probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm is 0.01715.

### What is normal distribution?

A normal distribution is a probability distribution that has been symmetrical around this mean, with most observations clustering around the central peak and probabilities tapering off evenly in both directions.
Now, according to the question,
The formula for normal distribution is;
z = (x – μ)/(σ/√s)
x is the sample size (= 96)
μ = standard mean (= 92)
σ = standard deviation (= 10)
s = random sample (= 28)
Substituting all the values in the equation;
z = (96 – 92)/(10/√28)
z = 2.117
Now, calculate the probability;
P(X > 96) = 1 – P(X ≤ 96)
= 1 – P(X ≤ 2.117)
= 1 – 0.98285
P(X > 96) =  0.01715
Therefore, the probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm is 0.01715.
To know more about the normal distribution, here
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The complete question is-
The reading speed of a second grade students in a large city is approximately normal with a mean of 92 words per minute and a standard deviation of 10 wpm. What is the probability that a random sample of 28 second grade students from the city results in a mean reading rate of more than 96 wpm?