A manufacturer packages coffee beans in 50 kg
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Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
- It 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, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem:
- Mean of 62 mph, hence
.
- Standard deviation of 5 mph, hence
.
- Sample of 50 cards, hence
The probability of a sample of 50 cars recording an average speed of 66 mph or higher is <u>1 subtracted by the p-value of Z when X = 66</u>, hence:
By the Central Limit Theorem
has a p-value of 1.
1 - 1 = 0.
There is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.
A similar problem is given at brainly.com/question/24663213