We have here as as
, then the values are.
s=8.7
For the resulting of the test by the teacher he had,
With all of this dates to make the comparition we use the formula for Z values, that is
We know moreover that = 0.052.
To find we need to find
Searching in the table of Normal Distribution for Z, and making the lecture we find that z_{critic} is, 1.95.
Answer:
B. 0.0099
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 roblem, we have that:
Probability of being out of control.
Less than 8.25 pounds, which is the pvalue of Z when X = 8.25. So
By the Central Limit Theorem
has a pvalue of 0.0099.
So the correct answer is:
B. 0.0099