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# 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.
(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
(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