MATHEMATICS COLLEGE

A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 155 while the ACT scores have a mean of 22 and a standard deviation of 4. Assuming the performance on both tests follows a normal distribution, determine which test the student did better on.

Answers

Answer 1

Answer:

Answer:

Due to the higher z-score, he did better on the SAT.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

$Z = (X - \mu)/(\sigma)$

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.

Determine which test the student did better on.

He did better on whichever test he had the higher z-score.

SAT:

Scored 1070, so $X = 1070$

SAT scores have a mean of 950 and a standard deviation of 155. This means that $\mu = 950, \sigma = 155$ .

$Z = (X - \mu)/(\sigma)$

$Z = (1070 - 950)/(155)$

$Z = 0.77$

ACT:

Scored 25, so $X = 25$

ACT scores have a mean of 22 and a standard deviation of 4. This means that $\mu = 22, \sigma = 4$

$Z = (X - \mu)/(\sigma)$

$Z = (25 - 22)/(4)$

$Z = 0.75$

Due to the higher z-score, he did better on the SAT.

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Answers

Answer:

Step-by-step explanation:

tommy has a car with a 22-gallon gas tank that yields 16 miles per gallon. How far can he drive on a full tank of gas?

Answers

Answer:

On a full tank of gas, Tommy can drive a distance:

D = 22 x 16 = 352 miles

Hope this helps!

Answer:352 miles

Step-by-step explanation:

1 gallons for 16 miles

22 gallons for ______

For 22 gallons 22x16=352 miles

Gloria earned a total of $810 over the summer. She earned $162 babysitting and the restfrom mowing lawns. Which bar model and solution represent x, the amount of money Gloria
earned mowing lawns?

Answers

Let x represent the amount of money Gloria earned mowing lawns.

We have been given that Gloria earned a total of $810 over the summer. She earned $162 babysitting and the rest from mowing lawns.

The total amount earned by Gloria would be amount earned from baby sitting and lawn mowing that is $x+162$ .

Now we will equate total earnings of Gloria by 810 as:

$x+162=810$

$x+162-162=810-162$

$x=648$

Therefore, Gloria earned $648 from mowing lawns.

Answer:

Gloria earned $648 from mowing lawns

Step-by-step explanation:

Problems1) Paul runs 4 miles in 28 minutes. If he runs each mile at the same pace,
what is his rate in minutes per mile?
1 point
Your answer

Answers

Answer:

Step-by-step explanation:

You must divide 28 by 4 which equals 7.

Thirty 7th graders were surveyed and asked their favorite sport. The results showed that 15 liked football, 7 liked baseball, 5 like basketball, and 3 like soccer. What generalization can not be made?Soccer is the least favorite sport.
Half of the students like football.
The students would prefer to play sports over going to school.
None of the students like tennis.