Question

At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 21 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.
Part (a) In words, define the Random Variable X.
the number of fencers that do not use the foil as their main weaponthe different types of weapons the number of fencers at The Fencing Centerthe number of fencers that do use the foil as their main weapon
Part (b) List the values that X may take on.
X = 0, 1, 2, . . ., 60X = 1, 2, 3, . . ., 21 X = 0, 1, 2, . . ., 21X = 1, 2, 3, . . ., 60
Part (c) Give the distribution of X.
X ~
,
Part (d) How many fencers are expected to not use the foil as their main weapon? (Round your answer to the nearest whole number.)
fencers
Part (e) Find the probability that eleven do not use the foil as their main weapon. (Round your answer to four decimal places.)
Part (f) Based on numerical values, would you be surprised if all 21 did not use foil as their main weapon?
Yes. The probability of all 21 fencers not using the foil as their main weapon is small (less than 1%).No. The probability of all 21 fencers not using the foil as their main weapon is large (more than 10%).

Answer 1

Answer:

A.) the number of fencers that do not use the foil as their main weapon

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

C.) X ~ p(X) ; 21 ~ 0.4

D.) 21 ~ 0.4

E.) 0.0895

F.) Yes. The probability of all 21 fencers not using the foil as their main weapon is small (less than 1%)

Step-by-step explanation:

A.) since it is reported that 60% of fencers use the foil as their main weapon ;

The random variable (x) : number of fencers that do not use foil as their main weapon ;

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

B.) values that X may take on :

Sample size = 21 ;

X : 0, 1, 2,..., 21

The distribution of X

X ~ B ; X ~ p(X) ; 21 ~ 0.4

Part (d) How many fencers are expected to not use the foil as their main weapon?

X * p(x)

21 * 0.4

= 8.4

= 8 (nearest whole number)

Part (e) Find the probability that eleven do not use the foil as their main weapon.

P(x = 11)

Using the binomial probability relation :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

P(x = 11) = 21C11 * 0.4^11 * 0.6^10

P(x = 11) = 0.0895

Part (f) Based on numerical values, would you be surprised if all 21 did not use foil as their main weapon?

P(x = 21) = 21C21 * 0.4^21 * 0.6^0

P(x = 21) = < 0.00001 ( approximately 0)

Hence, based on this very low value which is almost equal to 0 ; it will be surprising if all 21 do not use foil as their main weapon