Question

What is the probability that a random sample of 12 second grade students from the city in a mean reading rate of more than 96 words per minute?

Answer 1

Complete Question

The reading speed of second grade students in a large city is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.

What is the probability that a random sample of 12 second grade students from the city in a mean reading rate of more than 96 words per minute?

Answer:

$P(\=x >96 )=0.01884$

Step-by-step explanation:

From the question we are told that:

Sample size $n=12$

Sample mean $\=x =90$

Standard Deviation $\sigma=10$

Generally

$\sigma_x=\frac{\sigma}{\sqrt{10}}$

$\sigma_x=\frac{10}{\sqrt{12}}$

$\sigma_x=2.887$

Generally the equation for P(\=x >96 ) is mathematically given by

$P(\=x >96 )=P(Z>\frac{\=x-\mu_x}{\sigma_x})$

$P(\=x >96 )=P*(Z>\frac{90-96}{2.887})$

$P(\=x >96 )=1-P(Z<2.08)$

$P(\=x >96 )=1-0.98116$

$P(\=x >96 )=0.01884$