Question

Suppose that the average length of stay in a U.S. hospital is approximately normally distributed and said to be 2.4 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital. Which is more likely to occur:

1. An individual stayed more than 3 days.
2. The average stay of 80 women was more than three days.

Please explain your choice. Use terms discussed in Unit 2: Central Limit Theorem, standard deviation, standard error, etc.

Sketch and label a picture that is associated with the following situations and then find the relevant probability or z-score. Please show your work or describe how you arrived at each response. I have provided places to upload your sketches or you can include them in your sketch work you submit after the exam.

1. P( z≤−0.48z≤-0.48 OR z≥1.73z≥1.73 )
   
2. Find the z-score such that the area under the standard normal curve to the right is 0.001.
   

Answer 1

An individual stayed more than 3 days.

z = (x - µ)/σ = (3 - 2.4)/0.9 = 0.67

Probability = 0.2525

The average stay of 80 women was more than three days.

z = (x - µ)/σ/√n = (3 - 2.4)/0.9/√80 = 5.96

Probability = 0.0000

An individual stayed more than 3 days is more likely to occur.

The curve is:

Probability = 1 - 0.6426 = 0.3574

The curve is:

z-score = 3.090

Please give me a thumbs-up if this helps you out. Thank you!