Cholesterol levels for a group of women aged 30-39 follow an approximately normal distribution with mean 190.14 milligrams per deciliter (mg

Question

Cholesterol levels for a group of women aged 30-39 follow an approximately normal distribution with mean 190.14 milligrams per deciliter (mg/dl). Medical guidelines state that women with cholesterol levels above 240 mg/dl are considered to have high cholesterol and about 9.3% of women fall into this category.

1. What is the Z-score that corresponds to the top 9.3% (or the 90.7-th percentile) of the standard normal distribution? Round your answer to three decimal places.

2. Find the standard deviation of the distribution in the situation stated above. Round your answer to 1 decimal place.

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Savannah 1 month 2021-10-17T14:55:22+00:00 1 Answer 0 views 0

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    2021-10-17T14:56:26+00:00

    Answer:

    Step-by-step explanation:

    Hello!

    X: Cholesterol level of a woman aged 30-39. (mg/dl)

    This variable has an approximately normal distribution with mean μ= 190.14 mg/dl

    1. You need to find the corresponding Z-value that corresponds to the top 9.3% of the distribution, i.e. is the value of the standard normal distribution that has above it 0.093 of the distribution and below it is 0.907, symbolically:

    P(Z≥z₀)= 0.093

    -*or*-

    P(Z≤z₀)= 0.907

    Since the Z-table shows accumulative probabilities P(Z<Z₁₋α) I’ll work with the second expression:

    P(Z≤z₀)= 0.907

    Now all you have to do is look for the given probability in the body of the table and reach the margins to obtain the corresponding Z value. The first column gives you the integer and first decimal value and the first row gives you the second decimal value:

    z₀= 1.323

    2.

    Using the Z value from 1., the mean Cholesterol level (μ= 190.14 mg/dl) and the Medical guideline that indicates that 9.3% of the women have levels above 240 mg/dl you can clear the standard deviation of the distribution from the Z-formula:

    Z= (X- μ)/δ ~N(0;1)

    Z= (X- μ)/δ

    Z*δ= X- μ

    δ=(X- μ)/Z

    δ=(240-190.14)/1.323

    δ= 37.687 ≅ 37.7 mg/dl

    I hope it helps!

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