Gwen commutes to work. She commute is 35 miles every day. Top top Friday, she drives 28 mile farther than any kind of other day. Her full co

A rectangle-shaped prism has actually a size of 20 in., a broad of 2 in., and also a height of 3 1/4 in. The prism is filled with cubes that have

The producer of a weight-loss pill advertises that civilization who usage the pill lose, after ~ one week, an typical (mean) of 1.75 pound

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44.23% probability the the mean weight lose after one week on this pill for a random sample the 55 people will it is in 1.77 pounds or more

Step-by-step explanation:

To resolve this question, we require to recognize the regular probability distribution and the main limit theorem.

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Normal probability distribution

Problems of normally distributed samples are resolved using the z-score formula.

In a collection with average

*
and standard deviation
*
, the zscore of a measure X is given by:

*

The Z-score steps how many standard deviations the measure is from the mean. ~ finding the Z-score, we look in ~ the z-score table and also find the p-value connected with this z-score. This p-value is the probability that the worth of the measure is smaller sized than X, that is, the percentile that X. Subtracting 1 through the pvalue, we acquire the probability the the value of the measure is greater than X.

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Central border Theorem

The central Limit theorem estabilishes that, for a normally distributed random change X, with average

*
and standard deviation
*
, the sampling circulation of the sample way with size n deserve to be approximated to a normal distribution with mean
*
and also standard deviation
*
;

For a skewed variable, the main Limit theorem can additionally be applied, as lengthy as n is at least 30.

In this problem, we have that:

*

What is the probability that the typical weight loss after one main on this pill for a random sample that 55 people will be 1.77 pounds or more

This is 1 subtracted through the pvalue the Z when X = 1.77. So

*

By the main Limit Theorem

*

*

*

*
has a pvalue that 0.5577

1 - 0.5577 = 0.4423

44.23% probability that the average weight ns after one week on this pill because that a random sample of 55 people will it is in 1.77 pounds or more