Mathematics, 12.02.2020 02:52, kiaunarayne808

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.372 minute. The winning car, driven by Sam, finished in 185.85 minutes. The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes. Find their respective z-scores. Who had the more convincing victory? Sam had a finish time with a z-score of Karen had a finish time with a z-score of (Round to two decimal places as needed.) Which driver had a more convincing victory?

A. Sam had a more convincing victory because of a higher z-score.
B. Karen a more convincing victory because of a higher z-score.
C. Sam had a more convincing victory, because of a lower z-score.
D. Karen a more convincing victory because of a lower z-score.

Answers: 3

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answered: bferguson8956

Sam had a finish time with a z-score of -2.93.

Karen had a finish time with a z-score -1.91.

Sam had the more convincing victory.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

Sam:

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.372 minute. The winning car, driven by Sam, finished in 185.85 minutes.

So $\mu = 186.94, \mu = 0.372, X = 185.85$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{185.85 - 186.94}{0.372}$

Z = -2.93

Sam finishing time was 2.93 standard deviations below the mean.

Sam had a finish time with a z-score of -2.93.

Karen:

The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.

So $\mu = 110.7, \sigma = 0.115, X = 110.48$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{110.48 - 110.7}{0.115}$

Z = -1.91

Karen finishing time was 1.91 standard deviations below the mean.

Karen had a finish time with a z-score -1.91.

Who had the more convincing victory?

Sam finishing time was 2.93 standard deviations below the mean.

Karen finishing time was 1.91 standard deviations below the mean.

Sam finished more standard deviations below the mean than Karen, that is, he was faster relative to his competition than Karen.

So Sam had the more convincing victory.

answered: Guest

no, the equation would be invalid since they are both not equal.

step-by-step explanation:

here you got

4y-6+4y 2-9

first, you would simplify the equation on the form.

4y-6+4y 2-9

then, move all the terms that contains a y to the left and all the other terms to the right.

+4y-4y+-9-6

finally, you will simplify the left and the right side of the equation.

y=-3

answered: Guest

the equation for this situation is y=122+45. to solve the equation you would add 45 and 122 to get a total of 167lbs. in conclusion, grace's weight eight weeks ago was 167lbs.