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

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=(x-\mu)/(\sigma)`

For x= 51

`z=(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