# Statistics : The five-number summary below shows the grade

Subject: Mathematics / Statistics
Question
5. The five-number summary below shows the grade distribution of a STAT 200 quiz for a
sample of 1000 students.
Answer each question based on the given information, and explain your answer in each case.
(a) What is the interquartile range in the grade distribution?
(b) Which score band has the fewest students?
(i) 20 – 60
(ii) 60 – 75
(iii) 75 – 90
(iv) Cannot be determined
(c) How many students are in the score band between 75 and 100? 10. Assume random variable x follows a probability distribution shown in the table below.
Determine the mean and standard deviation of x. Show all work. Just the answer, without
supporting work, will receive no credit.
x -2 -1 0 1 2
P(x) 0.1 0.4 0.1 0.1 0.3
12. A research concludes that the number of hours of exercise per week for adults is normally
distributed with a mean of 3.5 hours and a standard deviation of 3 hours. Show all work. Just the
answer, without supporting work, will receive no credit.
(a) Find the 75th percentile for the distribution of exercise time per week. (round the answer to 2 decimal
places)
(b) What is the probability that a randomly selected adult has more than 5 hours of exercise per week?
(round the answer to 4 decimal places)
13. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500
and a standard deviation of 100. Show all work. Just the answer, without supporting work, will