Question

Use for questions 37-40: the 100-meter dash times in the girls track meet were normally distributed with a mean of 13 seconds and a standard deviation of 0.3 seconds.

lana finished the race in 13.2 seconds. if 84 other girls ran in the event, approximately how many runners did she beat?

Answer 1

Okay, here are the step-by-step solutions:

37) Lana's time was 13.2 seconds. The mean time was 13 seconds and the standard deviation was 0.3 seconds.

Since Lana's time was 13.2 seconds, we need to find out how many standard deviations her time is from the mean.

We calculate the z-score as:

z-score = (Lana's time - Mean time)/Standard deviation

= (13.2 - 13)/0.3

= 2

Since it is a normally distributed set of data, we can use the normal distribution table to find the percentage of girls who scored below Lana.

For a z-score of 2, the percentage below is 2.28%.

There were 84 other girls who ran in the event.

2.28% of 84 is 1.92 girls.

Rounding it off, we can say approximately 2 girls finished below Lana's time.

So the answer is: Approximately 2 runners did she beat.