Question

The mean number of words per minute (WPM) read by sixth graders is 81 with a standard deviation of 17 WPM. If 130 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 77.21 WPM? Round your answer to four decimal places.

Answer 1

The probability that the sample mean would be greater than 77.21 WPM = 0.9945

Explanation:

Mean number of Words per Minute = u = 81

Standard Deviation = s = 17

sample size = n = 130

Target value = x = 77.21

we can find the probability by converting x to z-score.

The formula for z-score =
`(x-u)/((s)/(√(n) ) )`

using given values, z-score =
`(77.21-81)/((17)/(√(130) ) )`

=> -2.54

using the z table, we can find the find the probability of -2.54, that is 0.9945.

Therefore, the probability that the sample mean would be greater than 77.21 WPM = 0.9945