Question

The time it takes NFL running backs to run the 40-yard dash follows a normal distribution with a mean time of 4.59 seconds and a standard deviation of 0.12 second. Let x = the time it takes an NFL running back to run the 40-yard dash. (Use the Empirical Rule. Write your answers as a percent.) (a) P(x < 4.83) Incorrect: Your answer is incorrect. % (b) P(4.35 < x < 4.83)

Answer 1

Here,

X ~ Normal(4.59, 0.12²)

Using empirical rule,

95% values of a normal distribution will lie between (mean - 2*standard deviation, mean + 2*standard deviation)

Here,

mean = 4.59

standard deviation = 0.12

So,

95% values of a normal distribution will lie between (mean - 2*standard deviation, mean + 2*standard deviation) = (4.59 - 2*0.12, 4.59 + 2*0.12) = (4.35, 4.83)

Percentage of values lie outside the interval (4.35, 4.83) is = (100 - 95)% = 5%

Percentage of values less than 4.35 is = 5/2 = 2.5%

a)

b)