Oscar scored a 45/50 on his most recent test what percent of the problems did oscar get correct?
1 answer:
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Answer:
73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce
Step-by-step explanation:
To solve this question, we need to understand 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.
In this problem, we have that:
What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?
This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So
X = 8.22
By the Central Limit Theorem
has a pvalue of 0.8665
X = 8.18
has a pvalue of 0.1335
0.8665 - 0.1335 = 0.7330
73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce
Answer: 3
Explanation: Absolute value means <em>distance from zero</em> on a number line. So far the absolute value of 3, we know that 3 is 3 units from zero on a number line so the absolute value of 3 is 3.
A. The linear equation is: y = 60x + 45
B. The graphed equation is shown in the attachment below.
<h3>What is a Linear Equation?</h3>A linear equation is defined as, y = mx + b, where the initial value = b; unit rate = m; x and y are the variables.
A. In this situation given, we have:
- Total cost = y
- Number of months = x
- Monthly charges = unit rate (m)= $60
- Initial value (b) = $45
Substituting the values into y = mx + b, we would have the equation as:
y = 60x + 45
B. The graph of the equation is shown in the image attached below.
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