I need help with this. 3x + 5= 35, x =
1 answer:
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Answer:
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, 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.
Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches.
This means that
Sample of 36:
This means that
Find the probability that they have a mean height greater than 72.3 inches.
This is 1 subtracted by the pvalue of Z when X = 72.3. So
By the Central Limit Theorem
has a pvalue of 0.9979
1 - 0.9979 = 0.0021
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
Complete question:
A student in an introductory statistics course investigated if there is evidence that the proportion of
milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are
green. She purchased a bag of each variety and her data are summarized in the following table:
Milk chocolate- Green:8 Not Green: 33 Total: 41
Dark Chocolate- Green: 4 Not green: 38 Total :42
a) Define the appropriate parameter(s) for this data.nd state the hypotheses for testing if the proportion of green M&M's differs for milk chocolate and dark chocolate M&M's.
b. The p-value is 0.32. Use this p-value to make a decision about these hypotheses with an alpha of 0.05. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence.
Step-by-step explanation:
a. = Proportion of milk chocolate M&M 's that are green
= Proportion of dark chocolate M&M 's that are green
≠
b. This p-value provides no evidence that the proportion of green candies differs for milk chocolate and dark chocolate M&M's