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Marrrta [24]
2 years ago
12

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.
Mathematics
1 answer:
antoniya [11.8K]2 years ago
8 0

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 = \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.

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

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

Z = \frac{25 - 22}{4}

Z = 0.75

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

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Given that, according to sanitation departments report; the samount of garbage produced by 1 resident = 1.643 \times 10^3pound.

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To find that we just need to multiply the garbage produced by 1 resident with the population of the city.


Total garbage collected = (2.61 \times 10^5 ) * (1.643 \times 10^3 ) pounds

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2 years ago
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The condo costs $163,000, earns $2,986 per month, spends no more than 25% of her income, then if she pays $33,000 for the down payment, the remaining amount would be $130,000. Since 20% of the initial cost is only $32,600, she can adjust her down payment to 20.25% of the initial cost so that the annual payments would be less.
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To a survey of 290 newspaper reader, 181
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Question:

To a survey of 290 newspaper readers, 181 of them read the Daily Times, 142 Read the Guardian 117 read punch and each reads at least one of the three papers if 75 read the Daily Times, and the Guardian, 60 read the Daily Times and punch, and 54 read the Guardian and punch : Draw a Venn diagram to illustrate this information How many readers read All three papers ,Exactly two of the papers The Guardian alone?

Answer:

39 read all three news papers,72 Exactly two Papers & 52 reads  Guardian Alone

Step-by-step explanation:

We have given, A survey of 290 newspaper readers.

Who read the Daily times A=181  

Who read the Guardian times B=142  

Who read the punch C=117

Who read Daily Times and the Guardian A\cap B= 75

Who read Daily Times and the punch A\cap C=60

Who read Guardian and punch B\cap C=54

To find :

How many readers read All three papers, Exactly two of the papers The Guardian alone?

Solution :

Readers read all three papers is A\cap B\cap C

Total survey is given by,

Total = A+B + C- A\cap B- A\cap C - B\cap C+ A\cap B\cap C

290 = 181 + 142 + 117 - 75 -60 - 54 +A\cap B\cap C

290 =251+A\cap B\cap C

290-251=A\cap B\cap C

A\cap B\cap C=39

So, number of readers who read all three papers is 39.

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Answer:

D. The difference of the means is not significant because the re-randomizations show that it is within the range of what could happen by chance.

Step-by-step explanation:

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The best conclusion that can be made is - The difference of the means is not significant because the re-randomizations show that it is within the range of what could happen by chance.

As we know, in statistics, nothing happens by chance. So, this option is correct.

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