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. complete parts​ (a) through​ (f). ​(a) what is the probability a randomly selected student in the city will read more than 96 words per​ minute?

Answer 1

Answer: 0.2743

Step-by-step explanation:

Given : The reading speed of second grade students in a large city is approximately​ normal, with a mean of $\mu=90$ words per minute​ (wpm) and a standard deviation of $\sigma=10$ wpm.

Let x be the random variable that represents the reading speed of second grade students.

z-score : $z=\dfrac{x-\mu}{\sigma}$

For x= 96 words per​ minute

$z=\dfrac{96-90}{10}=0.6$

Now, the probability a randomly selected student in the city will read more than 96 words per​ minute will be :-

$P(x>96)=P(z>0.6)=1-P(\leq0.6)\\\\=1- 0.7257469=0.2742531\approx0.2743$

Hence, the probability a randomly selected student in the city will read more than 96 words per​ minute = 0.2743

Answer 2

The probability is 0.2743.

Calculating the z-score for this time, we have:

z = (X-μ)/σ
z = (96-90)/10 = 6/10 = 0.6

Using a z-table (http://www.z-table.com) we see that the area to the left of this, less than this score, is 0.7257.  This means the area greater than this would be 1-0.7257 = 0.2743.