Round 4 decimal places or give answers in scientific notation if necessary.
1. It is believed to be true that 15% of the U.S. population is left-handed. You randomly select 10 people. Let x represent the number of left-handers.
a. Construct a binomial distribution. (4 decimal places or give answers in scientific notation if necessary.)
b. Find the probability that exactly 8 people are left-handed.
c. Find the probability that less than 3 people are left-handed.
d. Find the probability that at least 1 person is left-handed.
e. Find the mean of the binomial distribution.
f. Find the standard deviation of the binomial distribution.
2. Complete the following sentence:
a. In our class data, we surveyed a TOTAL (males and females) of _____ (n) students and found that _____ (x) were left-handed.
b. Assuming that 15% of the population is left-handed, find the probability of surveying n students and getting exactly x "lefties" (Use the numeric values for n and x from our class data.)
c. We noted that an event that occurs with a probability of 0.05 or less is considered unusual. Is the number of "lefties" (x) in our data unusual? (State yes or no)
d. Assuming that 15% of the population is left-handed and we surveyed a total of (n) students, calculate the mean.
e. Using the mean from part d, should we have expected more or less "lefties" in our class data
Female Data to use for above
|
Student #
|
Gender
|
Height
|
Shoe
|
Age
|
Hand
|
|
1
|
F
|
68
|
8.5
|
20
|
R
|
|
2
|
F
|
60
|
5.5
|
27
|
R
|
|
3
|
F
|
64
|
7
|
31
|
R
|
|
4
|
F
|
67
|
7.5
|
19
|
R
|
|
5
|
F
|
65
|
8
|
20
|
R
|
|
6
|
F
|
66
|
9
|
29
|
R
|
|
7
|
F
|
62
|
9.5
|
30
|
L
|
|
8
|
F
|
63
|
8.5
|
18
|
R
|
|
9
|
F
|
60
|
5
|
19
|
L
|
|
10
|
F
|
63
|
7.5
|
42
|
R
|
|
11
|
F
|
61
|
7
|
20
|
R
|
|
12
|
F
|
64
|
7.5
|
17
|
R
|
|
13
|
F
|
65
|
8
|
19
|
R
|
|
14
|
F
|
68
|
8
|
19
|
R
|
|
15
|
F
|
63
|
7.5
|
18
|
R
|
|
16
|
F
|
62
|
7.5
|
19
|
R
|
|
17
|
F
|
64
|
7
|
23
|
R
|
|
18
|
F
|
72
|
11
|
28
|
R
|
|
19
|
F
|
62
|
8
|
20
|
R
|
|
20
|
F
|
59
|
6.5
|
29
|
R
|
|
21
|
F
|
64
|
8.5
|
19
|
R
|
|
22
|
F
|
68
|
9.5
|
23
|
R
|
|
23
|
F
|
65
|
9.5
|
34
|
R
|
|
24
|
F
|
63
|
8
|
27
|
R
|
|
25
|
F
|
65
|
8
|
23
|
R
|
|
26
|
F
|
62
|
7.5
|
30
|
R
|
|
27
|
F
|
67
|
7.5
|
31
|
L
|
|
28
|
F
|
66
|
9
|
37
|
R
|
|
29
|
F
|
61
|
6
|
24
|
R
|
|
30
|
F
|
61
|
6.5
|
46
|
R
|
|
31
|
F
|
68
|
8
|
20
|
R
|
|
32
|
F
|
63
|
7.5
|
42
|
R
|
|
33
|
F
|
63
|
5.5
|
33
|
R
|
|
34
|
F
|
58
|
5
|
20
|
R
|
|
35
|
F
|
65
|
8
|
44
|
R
|
|
36
|
F
|
69
|
9
|
28
|
R
|
|
37
|
F
|
68
|
9
|
20
|
R
|