Suppose X is the time it takes a randomly chosen clerical worker in an office to type and send a standard letter of recommendation. Suppose X has a normal distribution, and assume the mean is 10.5 minutes and the standard deviation 3 minutes. You take a random sample of 50 clerical workers and measure their times. What is the chance that their average time is less than 9.5 minutes?

The chance that their average time is less than 9.5 minutes is 0.0094

Step-by-step explanation:

X is the time it takes a randomly chosen clerical worker in an office to type and send a standard letter of recommendation

We are given that X has a normal distribution

Mean = 10.5 minutes

Standard deviation = 3 minutes

n = 50

We are supposed to find the chance that their average time is less than 9.5 minutes i.e. P(X<9.5 minutes)

Formula :

Z = −2.35

Refer the z table for p value

p value=0.0094

So, P(X<9.5)=P(Z<−2.35)=0.0094

Hence  the chance that their average time is less than 9.5 minutes is 0.0094.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

p

step-by-step explanation: