Question

Andy and Jim are going to compete in the 100-meter dash against each other. Let AAA be the time it takes Andy to complete the race, and JJJ be the time it takes Jim to complete the race. Based on previous results, they know that \mu_A=11.5μ A ​ =11.5mu, start subscript, A, end subscript, equals, 11, point, 5 seconds and \sigma_A=1σ A ​ =1sigma, start subscript, A, end subscript, equals, 1 second. They also know that \mu_J=10.5μ J ​ =10.5mu, start subscript, J, end subscript, equals, 10, point, 5 seconds and \sigma_J=0.5σ J ​ =0.5sigma, start subscript, J, end subscript, equals, 0, point, 5 seconds.

Answer 1

Answer:

μd= 1 second

σd= square root (1.25) = √1.25 seconds= 1.1180 seconds

Step-by-step explanation:

Assume that their times are independent. Let DDD be the difference between their times in a random 100-meter dash (D=A-J)(D=A−J)left parenthesis, D, equals, A, minus, J, right parenthesis.

Find the standard deviation of DD

The mean difference is found out by subtracting the individual means.

The mean difference = μd= μA- μJ= 11.5- 10.5= 1 second

The difference standard deviation is given by the square root of sum of the individual variances divided by n. But here n1= n2= 1

σd = sqrt( σ1² / n1 + σ2 ²/ n2 )

First we calculate the variances.

Variance is the square of the standard deviation.

The variance of Andy =σA²= 1²= 1

The variance of Jim =σJ²= (0.5)²= 0.25

The standard deviation difference= σd= √σ²A+ σ²J/1= √1+ 0.25/1= √1.25/1 = √1.25 seconds = 1.1180 seconds