5. The frequency distribution below shows the distribution of average seasonal r

Question

5. The frequency distribution below shows the distribution of average seasonal rainfall in San Francisco, Page 2 of 8 STAT 200: Introduction to Statistics Final Examination, Summer 2018 OL1/US1 as measured in inches, for the years 1967-2017, (Show all work. Just the answer, without supporting work, will receive no credit Season Rainfall (in Inches) 0-9.99 10-19.99 20-29.99 30 30.99 40-40.99 Total Cumulative Relative Frequency 0.84 0.98 1.00 50 (a) Why is it appropriate to use a grouped frequency distribution for this data? (b) Complete the frequency table with frequency and cumulative relative frequency. Express the cumulative relative frequency to two decimal places. (c) What percentage of season in this sample has a seasonal rainfall between 0 and 19.99 inches, (d) Which of the following seasonal rainfall groups does the median of this distribution belong to? 10-19.99, 20-29.99, or 30-39.992 Why? 6. Consider selecting one card at a time from a 52-card deck. What is the probability that the first card is a diamond and the second card is also a diamond? Express the probability in fraction format. (Note: There are 13 diamonds in a deck of cards) (Show all work. Just the answer, without supporting work, will receive no credit.) (a) Assuming the card selection is with replacement (b) Assuming the card selection is without replacement. 7. Mimi has eight new summer outfits. She plans to pack three of the new summer outfits in her trip to Tokyo. (a) How many different ways can the three summer outfits be selected? (b) Please describe the method used and the reason why it is appropriate for answering the question. Just the answer, without the description and reason, will receive no credit. 8. A business man necds to visit clicnts in 7 different cities. (a) How many different routes can he take? (b) Please describe the method used and the reason why it is appropriate for answering the question. Just the answer, without the description and reason, will receive no credit.

Explanation / Answer

1)

a)

since we are measuring many values for example if we take each value as a seperate entry we will have lots of rows with very less data.

b)

we calculate the cumulative frequency as probabilty *50

we then subrtact the smaller bucket from the one just below to get the individual frequency

c)

44% as from the table

d)

10-19.99 is the cumulative as ~50% of the people lie there

6)

without replacement

numbe of ways of a diamond 13c1 12c1

numner of ways of to selecting 2 cards 52c1 51c1

so probability = 13*12/52*51 = 0.05882353

with replacement

(13/52)^2 = .0625

7)

n of ways of selecting 3 outfits = 8c3

freq cumulative 0-9.99 1 0.02 10-19.99 22 0.44 20-29.99 19 0.84 30-39.99 7 0.98 40-49.99 1 1 total 50

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