Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately 4 hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs. Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability.

And we can use the z score formula given by:

And using the z score we have:

And we can use the normal standard distribution table or excel in order to find the probabilities and we got:

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the time it takes her to complete one review, and for this case we know the distribution for X is given by:

Where and

And we select a sample size of n =16. Since the dsitribution for X is normal then the distribution for the sample mean is also normal and given by:

For this case we want to find this probability:

And we can use the z score formula given by:

And using the z score we have:

And we can use the normal standard distribution table or excel in order to find the probabilities and we got:

The graph illustrating the problem is on the figure attached.

do you mean add both of the equations together

because if you do the answer is 10x-5

step-by-step explanation:

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (