Question

Suppose the weight of linebackers in the National Football League (NFL) is normally distributed with a mean of 246 pounds and a standard deviation of 5.1 pounds.

a. What is the probability that a randomly selected NFL linebacker will weight less than 250 pounds? Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places. Probability = ?

b. What is the probability that a randomly selected NFL linebacker will weight more than 235 pounds? Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places. Probability = ?

c. What is the probability that a randomly selected NFL linebacker will weight between 237 pounds and 247 pounds? Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places. Probability =?

Answer 1

Given,

= 246 , = 5.1

We convert this to standard normal as

P(X < x) = P(Z < (x - ) / )

a)

P(X < 250) = P(Z < (250 - 246) / 5.1)

= P(Z < 0.78)

= 0.7823

b)

P(X > 235) = P(Z > 235 - 246 / 5.1)

= P(Z > -2.16)

= P(Z < 2.16)

= 0.9846

c)

P(237 < X < 247) = P(X < 247) - P(X < 237)

= P(Z < (247 - 246) / 5.1) - P(Z < (237 - 246) / 5.1)

= P(Z < 0.20) - P(Z < -1.76)

= 0.5793 - 0.0392

= 0.5401