Stanley drove his car on a business trip when he left, the mileage was 840 miles, and when he returned, the mileage was 1,200 mi
1 answer:
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Using the normal distribution and the central limit theorem, it is found that there is a 0.0284 = 2.84% probability of finding a sample mean mass of 695g or below.
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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 establishes 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.
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- Mean of 700g means that
- Standard deviation of 21g means that
- Sample of 64, thus
- <u>For the sampling distribution of the sample mean</u>, the standard deviation is of
The probability of finding a sample mean mass of 695g or below is the p-value of Z when X = 695, thus:
By the Central Limit Theorem
has a p-value of 0.0284.
0.0284 = 2.84% probability of finding a sample mean mass of 695g or below.
A similar problem is given at brainly.com/question/22934264
Answer:
Length of package can be = 22 inches
Step-by-step explanation:
Given:
For a package to qualify for a certain postage rate, the sum of its length and girth cannot exceed 85 inches
To find length of package when girth of package is = 63 inches
Solution:
Let length of package be = inches
Let girth length of package be = inches
Sum of length and girth of package = inches
To qualify for a certain postage rate the sum of length and girth should not exceed 85 inches.
Thus, the inequality representing the situation can be given as:
We are given girth of package is = 63 inches
So, inequality to find length would be:
Subtracting both sides by 63.
inches
So, length should not exceed 22 inches in order to qualify.
Thus, the maximum length of package to qualify for the postal rate must be = 22 inches