Question

Q1

Two of your friends each received the results of their first midterm exam this term.

• Maddy's score on the Spanish exam was 22.5 points. The distribution of Spanish exam scores was normal (bell-shaped) with an average score of 19 points (out of 25 points possible) and a standard deviation of 1.5 points.
• Max's score the the math exam was 72 points. The distribution of math exam scores was uniform over the range of 20 to 80 points, with a mean of 50 points and a standard deviation of 17.32 points.

Over dinner your friends begin discussing their results, each claiming they did better on their exam. They remember you are taking Stats 250 this term and turn to you for help to resolve the question: Who did better on their midterm exam?

Write a brief explanation to address this question from a statistical view making use of the corresponding exam distributions. As your friends have not taken Stats 250 yet, you will want to communicate your findings in a reasonable way.

Q2

The Centers for Disease Control and Prevention reported that 20% of all preschool children lack required immunizations. A random sample of preschool children will be selected. Let X = the number of sampled preschool children without immunizations.

Now use the normal approximation to the binomial to compute the approximate probability that at most 8 of the 64 sampled preschool children will lack the required immunizations. Show all your work and be sure to include (upload) an image (hand sketch or shiny app) that shows the area of the approximate probability using the normal approximation. (Note: as always, include your name and a title for your image or sketch.)

Answer 1

1)
higher the z-score, better is the performance
z =(X - mean)/sd

for Maddy
z = (22.5 - 19)/1.5 =
= 3.5/1.5
= 2.333333

for Max
z =(72 - 50)/ 17.32= 1.27

since z-score of Maddy is larger

Maddy performed better