The right answer is 118.
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PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
2 answers:
<h3>Answer: C) 98</h3>
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Explanation:
Let x be the next test grade. It ranges from 0 to 100, inclusive of both endpoints.
The original set {87,92,90,84,88,91} becomes {87,92,90,84,88,91,x} after adding on that score.
We have 7 scores now. We find the average by adding up those seven scores and dividing by 7.
average = (sum of the scores)/(number of scores)
average = (87+92+90+84+88+91+x)/7
average = (532+x)/7
We want the average to be 90 or higher, so we would then have these steps
This means Edgar must score a 98 or higher on the seventh test in order for his overall average to be 90 or higher.
In other words, the lowest test score he can get is a 98.
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Extra info (optional section):
Let's say Edgar gets the highest score possible.
So he gets x = 100
This would mean
average = (87+92+90+84+88+91+x)/7
average = (532+x)/7
average = (532+100)/7
average = 632/7
average = 90.2857 which is approximate
We can see that his overall average would stick to 90 if the teacher is rounding to the nearest whole number.
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Answer:
a) 18.94% probability that the sample mean amount purchased is at least 12 gallons
b) 81.06% probability that the total amount of gasoline purchased is at most 600 gallons.
c) The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.
Step-by-step explanation:
To solve this question, we use the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sums, we can apply the theorem, with mean and standard deviation
In this problem, we have that:
a. In a sample of 50 randomly selected customers, what is the approximate probability that the sample mean amount purchased is at least 12 gallons?
Here we have
This probability is 1 subtracted by the pvalue of Z when X = 12.
By the Central Limit theorem
has a pvalue of 0.8106.
1 - 0.8106 = 0.1894
18.94% probability that the sample mean amount purchased is at least 12 gallons
b. In a sample of 50 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at most 600 gallons.
For sums, so
This probability is the pvalue of Z when X = 600. So
has a pvalue of 0.8106.
81.06% probability that the total amount of gasoline purchased is at most 600 gallons.
c. What is the approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers.
This is X when Z has a pvalue of 0.95. So it is X when Z = 1.645.
The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.