Question

12. In a recent race, the finish times formed a normal distribution with a mean of 210 minutes and a standard deviation of 25 minutes.

      a)Find the z-score of Jose, who finished in 190 minutes.

      b)Find the z-score of Estella, who finished in 270 minutes

      c) What is the probability that a racer finished in less than 180 minutes?

      d)What is the probability a racer finished between 190 and 225 minutes?

Answer 1

Solution :

Given that ,

mean = = 210

standard deviation = = 25

a)

x = 190

z = (x - ) /

= ( 190 - 210 ) / 25

= -0.8

b)

x = 270

z = (x - ) /

= ( 270 - 210 ) / 25

= 2.4

c)

P(x < 180) = P((x - ) / < (180 - 210) / 25)

= P(z < -1.2)

= 0.1151

Probability = 0.1151

d)

P(190 < x < 225) = P((190 - 210)/ 25) < (x - ) /  < (225 - 210) / 25) )

= P( -0.8 < z < 0.6)

= P(z < 0.6) - P(z < -0.8)

= 0.7257 - 0.2119

= 0.5138

Probability = 0.5138