Question

A study of 12,000 able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11 minutes and standard deviation 0.74 minute. Choose a student at random from this group and call his time for the mile Y.

(a) Say in words what the meaning of P(Y ≥ 9.5) is. (CHOOSE A FOLLOWING ANSWER)

ANSWER A: P(Y ≥ 9.5) is the probability that the student runs the mile in more than 9.5 minutes.

ANSWER B: P(Y ≥ 9.5) is the probability that the student runs the mile in 9.5 minutes or more.

ANSWER C: P(Y ≥ 9.5) is the event that the student runs the mile in 9.5 minutes or more.

ANSWER D: P(Y ≥ 9.5) is the event that the student runs the mile in more than 9.5 minutes.

What is this probability? (Round your answer to four decimal places.)

(b) Write the event "the student could run a mile in less than 5.2 minutes" in terms of values of the random variable (CHOOSE A FOLLOWING ANSWER)

ANSWER A: Y. P(Y < 5.2)

ANSWER B: Y ≤ 5.2 P(Y ≤ 5.2)

ANSWER C: P(Y = 5.2)

ANSWER D: Y < 5.2

What is the probability of this event? (Round your answer to four decimal places.)

Answer 1

a)  

ANSWER B: P(Y ≥ 9.5) is the probability that the student runs the mile in 9.5 minutes or more.

µ =    7.11                  
σ =    0.74                  
                      
P ( X ≥   9.5   ) = P( (X-µ)/σ ≥ (9.5-7.11) / 0.74)              
= P(Z ≥   3.23   ) = P( Z <   -3.230   ) =    0.0006 (answer)

b)

ANSWER D: Y < 5.2

P( X < 5.2   ) = P( (X-µ)/σ < (5.2-7.11) /0.74)      
=P(Z < -2.58   ) =   0.0049   (answer)