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IB Math SL Year 2
Name: ____________________________
3-4 Binomial Distributions Homework
1. A supermarket records the amount of money d spent by customers in their store during a busy period. The
results are as follows:
Money in $ (d)
Number of customers (n)
0–20
20–40
40–60
60–80
24
16
22
40
80–100 100–120 120–140
18
10
4
(a) Find an estimate for the mean amount of money spent by the customers, giving your answer to the
nearest dollar ($).
(b)
Complete the following cumulative frequency table
Money in $ (d)
<20
<40
Number of customers (n)
24
40
(c)
<60
<80
< 100
< 120
< 140
The time t (minutes), spent by customers in the store may be represented by the equation
t=
(i)
2d
2
3
+ 3.
Use this equation and your answer to part (a) to estimate the mean time in minutes spent by
customers in the store.
2. The table shows the scores of competitors in a competition.
Score
10
20
30
40
50
Number of competitors
with this score
1
2
5
k
3
The mean score is 34. Find the value of k.
IB Math SL Year 2
3. A set of data is
18, 18, 19, 19, 20, 22, 22, 23, 27, 28, 28, 31, 34, 34, 36.
The box and whisker plot for this data is shown below.
(a) Write down the values of A, B, C, D and E.
A = ......
B = ......
C= ......
D = ......
E = ......
(b) What is the range of this data?
4. Consider the data set: 35, 65, 84, 27, 66.
(a) What is the standard deviation?
(b) What is the variance?
5. Ms. DeGrazia bought candies at the store yesterday! She wanted to find out the following information. For
each variable, determine if it is quantitative or qualitative. If quantitative, identify discrete or continuous.
Circle all that apply:
a) Number of colored candied in the box. quantitative or qualitative ---- discrete or continuous
b) Colors of different candies in a box.
quantitative or qualitative ---- discrete or continuous
c) The weight of the candies in a box.
quantitative or qualitative ---- discrete or continuous
IB Math SL Year 2
6. We have an experiment where we drew 2 marbles from an urn containing 4 red and 6 black marbles. What is the
expected number of red balls?
7. Let X denote the product of the faces when two ordinary dice are thrown.
a. Draw a grid to show the sample space of X.
b. Tabulate the probability distribution of X.
c. Determine P(X=8)
d. Determine P(1<x<6)
8. Bag A contains 2 red balls and 3 green balls. Two balls are chosen at random from the bag without replacement.
Let X denote the number of red balls chosen. The
X
0
1
2
following table shows the probability distribution
for X
k
3
1
P(X = x)
10
10
6
(a) Show that k =
10
(b)
Calculate E(X), the mean number of red balls chosen.
2
9. A coin is biased so that when it is tossed the probability of obtaining a head is . The coin is tossed 25 times. Let X be
3
the number of heads obtained.
a) What is the expected value of X?
b) What is the probability that a heads is rolled exactly 15- times?
IB Math SL Year 2
10. What’s the probability of at least 3 in the probability distribution shown? Explain.
4. The probability that a telephone line is engaged at a company switchboard is 0.25. If the switchboard has 10 lines,
find the probability that
a) Exactly one half of the lines are engaged
b) At least three lines are free (not engaged) to 4 SF
6) You choose! Answer questions in one of the following columns below:
An unbiased dice is thrown 10 times. Let x be the number
of sixes obtained. Find:
a) The expected number of sixes
A frequent flyer finds that she is delayed at a particular
airport once in every 5 trips, on average. One year she
uses the airport on 22 occasions. Using a binomial model,
find,
a) The expected number of journeys that will be delayed at
the airport
b) The variance
b) Var(X)
c) The probability that she is delayed on fewer than 4
occasions
c) P(X<𝜇)
IB Math SL Year 2