STAT213 Midterm practice questions

Question 1

1200 people were asked how many charitable donations they made last year. This frequency table summarizes the results:

Class	Frequency	%	Cum. %
1 to 2	862	71.83%	71.83%
3 to 5	279	23.25%	95.08%
6 to 10	54	4.50%	99.58%
11 to 30	5	0.42%	100.00%

a) What percentage made fewer than 6 donations? (95.08%)

b) What percentage made more than 2 donations? (28.17%)

c) In which class would you find the median? (1 to 2)

d) Compute the group mean and group standard deviation. (mean = 2.4529; std. dev. = 1.9884)

Question 2

A survey had the following results:

75% of those who read The Globe & Mail have annual household incomes of at least $60,000.

12% of the respondents read The Globe & Mail.

16.7% of the respondents have annual household incomes of at least $60,000.

a) What percentage of the respondents either read The Globe & Mail or have annual household incomes of at least $60,000? (19.7%)

b) What percentage of those whose annual household income is under $60,000 do not read The Globe & Mail? (96.4%)

c) Does reading the Globe & Mail depend on the annual household income? (yes it does)

Question 3

A study of 2000 individuals was conducted to determine if a link exists between a person’s educational level and frequency of gambling. These were the results:

	Less than high school	Completed high school	Some post secondary	Completed post secondary	Total
Low	24	278	442	249	993
Moderate	54	375	214	133	776
High	62	128	16	25	231
Total	140	781	672	407	2000

a) What percentage of the individuals have at least some post-secondary education? (53.95%)

b) What percentage of the individuals gamble at either a low or moderate level? (88.45%)

c) Compute the percentage in each educational group that has a high level of gambling. Which educational group has the greatest likelihood of having individuals at a high level of gambling? Identify any trends as we progress from the lowest educational level to the highest. (see the key)

d) For each gambling category, compute the percentage of individuals who have at least some post-secondary education. Which gambling category has the greatest percentage of those with at least some post-secondary education? Are there any noticeable trends? (see the key)

Question 4

A train has 9 passengers. They have 8 stations to choose from. What is the probability that 4 choose one station, 2 choose another station and 3 choose three separate stations? (6.31%)

Question 5
Given this data set:

150.53	157.64	168.47	143.14	143.8
161.42	138.97	156.56	147.09
132.92	138.94	159.53	142.62

a) Which way is the data skewed? What is the degree of skewness? (cs = 0.64; slightly skewed right)

b) Does the data contain any outliers? (no)

Question 6

A vacation survey broke people into 3 income groups. The survey also asked if they took a trip on vacation last year and, if they did, if they traveled overseas. These were the results:

	% in income group	% who traveled	% who traveled overseas
High	13%	88%	52%
Middle	71%	64%	12%
Low	16%	8%	0%

a) What percentage overall took a trip on vacation last year? (58.16%)

b) What percentage overall traveled overseas? (11.4016%)

c) Of those who traveled, what percentage traveled overseas? (19.6%)

d) What percentage of those who traveled are from the middle income group? (78.13%)

Question 7

A box has 20 balls: 4 white, 5 black, 8 red and 3 blue. Four balls are chosen.

a) What is the probability that at least 2 of the balls are red? (53.46%)

b) If at least 2 balls are red, construct the distribution of the number of red balls. (see key)

Question 8

A deck of cards consists of the numbers 1 through 10, each number being of the colour red, blue, yellow, green or orange for a total of 50 cards. Six cards are chosen.

a) What is the probability the hand of six cards contains two pairs? (19.82%)

b) If the hand of six cards contains exactly 3 fours, what is the probability the hand contains a full house (3 of a kind plus a pair)? (25.37%)

Question 9

In a town, 40% of people watch hockey on TV on average.

a) If 12 people are randomly selected, what is the probability that no more than 1 of them watch hockey? (1.96%)

b) If 8 people are randomly selected, what is the probability that at least 6 of them watch hockey? (4.99%)

c) If 9 people are selected, what is the probability that exactly 4 of them watch hockey?

a) For this town of 1200, what is the fewest and most number of people who can be expected to watch hockey 99.7% of the time? Round to the nearest whole number. (429 and 531)

Question 10

The accident rate in a certain industry is 1 accident per 10,000 work hours on average.

a) For 50,000 work hours, what is the probability of no more than 1 accident? (4.04%)

b) For 75,000 work hours, what is the probability of at least 2 accidents? (99.53%)

c) What is the most number of accidents to be expected at least 88.89% of the time based on 75,000 work hours? Round to the nearest whole number. (16)