Answer :
The probability that the sample mean would be less than 142.2 wpm if 76 speed typists are randomly selected is 0.22575
The term probability is known as the possible number of occurring the event.
Here we have given that the mean number of words per minute (wpm) typed by a speed typist is 143 with a standard deviation of 12 wpm.
And we need to find the probability that the sample mean would be less than 142.2 wpm if 76 speed typists are randomly selected.
Here we know the following values from the given question,
=> mean = 143, standard deviation = 12
Then we have to calculate the z score as
=> z = (x-µ)/(σ/√n)
=> z = (150.2 - 143)/(12/√59)
=> z = 0.6
Now, the P-value from Z-Table:
P(x<150.2) = 0.72575
P(x>150.2) = 1 - P(x<150.2) = 0.27425
P(143<x<150.2) = P(x<150.2) - 0.5 = 0.22575
P( X > 150.2) = P(z > 2.048) = 0.0203
To know more about z - score here.
https://brainly.com/question/15016913
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