Question

Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution. What is the probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean is 47 words per minute and the standard deviation is 4 words per minute

Answer 1

Answer: 0.8413

Step-by-step explanation:

Given : Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution.

Mean : $\mu=47$

Standard deviation : $\sigma= 4$

Let x be the random variable that represents the typing speeds for the students.

The z-score :-

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

For x= 51

$z=\dfrac{51-47}{4}=1$

Using the standard normal distribution table ,the probability that a randomly selected student has a typing speed of less than 51 words per minute :-

$P(x<51)=P(z<1)\\\\= 0.8413447\approx 0.8413$

Hence, the probability that a randomly selected student has a typing speed of less than 51 words per minute = 0.8413