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IsabellaGracie
15.04.2020 •
Mathematics
Despite its nutritional value, seafood is only a tiny part of the American diet, with the average American eating just 16 pounds of seafood per year with a standard deviation of 3.2 pounds. Janice takes a random sample of 42 Americans. Find the probability that the sample mean seafood consumption of the 42 Americans is more than 17.5 pounds?
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Ответ:
0.12% probability that the sample mean seafood consumption of the 42 Americans is more than 17.5 pounds
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:
Find the probability that the sample mean seafood consumption of the 42 Americans is more than 17.5 pounds?
This is 1 subtracted by the pvalue of Z when X = 17.5. So
By the Central Limit Theorem
1 - 0.9988 = 0.0012
0.12% probability that the sample mean seafood consumption of the 42 Americans is more than 17.5 pounds
Ответ:
Step-by-step explanation:
x-intercept is for y = 0.
4x - 8y = 16
Put y = 0 to the equation, and solve for x:
4x - 8(0) = 16
4x - 0 = 16
4x = 16 divide both sides by 4
x = 4