J. V. Lin is an Olympic athlete competing in the women's javelin throw. The distances of her successful throws (in meters) are normally distributed with mean distance 60 meters and standard deviation 4 meters. (Round to the nearest percent and enter each of your answers as a whole number between 0 and 100.) (a) (2 points) What is the probability that on her first throw, J. v. Lin beats her mean distance? probability = %(b) (3 points) The current leader in the Olympics finals has thrown a distance of 66.5 meters. J. V. Lin has one attempt left to beat the leader's throw. What's the probability that Lin beats this throw? probability %

a) 50%

b) 5%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean distance 60 meters and standard deviation 4 meters.

This means that

(a) (2 points) What is the probability that on her first throw, J.v. Lin beats her mean distance?

This is, as a proportion, 1 subtracted by the pvalue of Z when X = 60. So

has a pvalue of 0.5

1 - 0.5 = 0.5

0.5*100% = 50%

50% probability.

(b) (3 points) The current leader in the Olympics finals has thrown a distance of 66.5 meters. J.V. Lin has one attempt left to beat the leader's throw. What's the probability that Lin beats this throw?

This is 1 subtracted by the pvalue of Z when X = 66.5. So

has a pvalue of 0.95

1 - 0.95 = 0.05

0.05*100% = 5%

5% probability.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40