Question

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected find the probability that he weighs between 170 and 220 pounds.

Answer 1

Answer:

The probability that he weighs between 170 and 220 pounds

P( 170 ≤ x≤ 200) = 0.3811

Step-by-step explanation:

Explanation:-

Given mean of the Population = 200 pounds

Given standard deviation of the Population = 50 pounds

Let 'X' be the random variable of the weights of college football players are normally distributed.

Let   x₁ = 170

$Z_{1} = \frac{x_{1} - mean}{S.D}$

$Z_{1} = \frac{170 - 200}{50}= -0.6$

Let   x₂ = 220

$Z_{2} = \frac{x_{2} - mean}{S.D}$

$Z_{2} = \frac{220 - 200}{50}= 0.4$

The probability that he weighs between 170 and 220 pounds.

P( 170 ≤ x≤ 200) = P(Z₁ ≤z≤Z₂)

                          =  P(-0.6 ≤z≤0.4)

                          = P(z≤0.4)-P(z≤-0.6)

                         =  0.5 + A(0.4) -(0.5 - A(-0.6)

                        =   A(0.4) + A(0.6)       A(-z) = A(z)

                       = 0.1554 +0.2257   ( check Areas in normal table)

                      = 0.3811

Conclusion:-

The probability that he weighs between 170 and 220 pounds

P( 170 ≤ x≤ 200) = 0.3811