Question

The weight of football players in the NFL is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

1. What is the probability that a randomly selected football player will weigh more than 243.75 pounds?
a. 0.4599
b. 0.0401
c. 0.9599
d. 0.5401

2. What is the probability that a football player will weigh less than 260 pounds?
a. 0.9918
b. 0.0528
c. 0.4918
d. 0.0082

3. What percentage of players will weigh between 150 to 250 pounds?
a. 34.13%
b. 95.4%
c. 47.72%
d. 68.26%

4. 95% of player weights are less than X pounds. Therefore, X is:
a. 241.25%
b. 206.25
c. 158.75
d. 193.75

Answer 1

Solution :

1.

P(x > 243.75) = 1 - P(x < 243.75)

= 1 - P[(x - ) / < (243.75 - 200) / 25)

= 1 - P(z < 1.75)

= 1 - 0.9599

= 0.0401

probability = 0.0401

option b.

2.

P(x < 260) = P[(x - ) / < (260 - 200) / 25]

= P(z < 2.4)

= 0.9918

probability = 0.9918

option a.

3.

P(150 < x < 250) = P[(150 - 200)/ 25) < (x - ) /  < (250 - 200) / 25) ]

= P(-2 < z < 2)

= P(z < 2) - P(z < -2)

= 0.9772 - 0.0228

= 0.9544

percentage = 95.4%

option b.

4.

Using standard normal table ,

P(Z < z) = 95%

P(Z < 1.65) = 0.95

z = 1.65

Using z-score formula,

x = z * +

x = 1.65 * 20 + 200 = 241.25%

option a.