Question

At the Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 26 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.

a. In words, define the Random Variable X.

b. List the values that X may take on.

c. Give the distribution of X.

d. How many fencers are expected to not use the foil as their main weapon? (Round your answer to the nearest whole number.)

e. Find the probability that fifteen do not use the foil as their main weapon.

f. Based on numerical values, would you be surprised if all 26 did not use foil as their main weapon?

Answer 1

a. In binomial distribution, x is number of successes in n repeated trials of a binomial experiment.

Hence here x is number of fences that do not use the foil as their main weapon.

b. x will take values from 0 to 26

c. Here we see that n=26 is constant, p=0.60 is same for all, events are independent and only two outcomes

Hence x is binomial distributed

x	P(x)=BINOMDIST(x,n,p,0)
0	0.0000
1	0.0000
2	0.0000
3	0.0000
4	0.0000
5	0.0000
6	0.0001
7	0.0005
8	0.0018
9	0.0054
10	0.0138
11	0.0301
12	0.0564
13	0.0912
14	0.1270
15	0.1524
16	0.1571
17	0.1386
18	0.1040
19	0.0657
20	0.0345
21	0.0148
22	0.0050
23	0.0013
24	0.0002
25	0.0000
26	0.0000

d. Expected value is

e. From c we can see that P(x=15)=0.1524