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?

Question

23-11-2022
Mathematics

Answered

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 :

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fahiskt9087 fahiskt9087 · Answer 1 · 2022-11-29T09:46:01-05:00

The correct answers listed below :

A)The percentage of fencers that don't utilize the foil as their primary weapon in A.

B.) X : 0, 1, 2, 3,..., 21

C.) X ~ p(X) ; 10.4

D.) 21 ~ 0.4

E.) 0.0895

F.) Yes. There is a low (less than 1%) chance that all 21 fencers will not use the foil as their primary weapon.

A.) Considering that 60% of fencers reportedly utilize the foil as their primary weapon;

Number of fencers who do not utilize foil as their primary weapon is the random variable (x);

( 100% - 60%) = (1 - 0.6) = 0.4

B.) Possible values for X include:

The sample size is 26;

X : 0, 1, 2,..., 26

The breakdown of X

X ~ B ; X ~ p(X) ; 26 *0.4

=10.4

How many fencers are anticipated to not utilize the foil as their primary weapon in Part (d)?

X * p(x) (x)

=26 * 0.4

= 8.4

= 8 (nearest whole number) (nearest whole number)

Determine the likelihood that eleven will not utilize the foil as their primary weapon in part (e).

P(x = 11)

Using the link between binomial probabilities:

P(x =x) is equal to nCx * px * (1 - p) (n - x)

P(x = 11) = 26C11 * 0.4^11 * 0.6^10

P(x = 11) = 0.0895

Would you be shocked if none of the 21 used foil as their primary weapon based on the numbers?

P(x = 26) = 26C21 * 0.4^26 * 0.6^0

P(x = 26) = < 0.00001 ( about 0) ( approximately 0)

It will therefore be surprising if all 26 do not employ foil as their primary weapon given this extremely low value, which is virtually equal to 0.

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