[1] The distribution of cholesterol levels of a population of 40-year-olds is approximately normally distributed with...

[1] The distribution of cholesterol levels of a population of 40-year-olds is approximately normally distributed with a mean of 220 mg/deciliter and a standard deviation of 12 mg/deciliter.

A. What is the approximate probability that a randomly selected 40-year-old from this population has a cholesterol level of more than 225 mg/deciliter? (Draw an appropriate diagram, find a z-score and indicate your calculator commands.)

B. A researcher takes a random sample of 16 people from this population and calculates the average cholesterol level.

i. What is the mean of the sampling distribution for a sample of this size? Briefly justify your answer.

ii. What is the standard deviation of the sampling distribution for a sample of this size? Briefly justify your answer.

iii. What is the shape of the sampling distribution for a sample of this size? Briefly justify your answer.

C. A researcher takes a random sample of 16 people from this population. What is the approximate probability that the sample mean cholesterol level for 16 random people will be greater than 225 mg/deciliter? (Draw an appropriate diagram, find a z-score and indicate your calculator commands.)

Solutions

Expert Solution

Here it is given that distribution is normal with mean=220 and standard deviation=12

A. We need to find

As distribution is normal we can convert x to z

. We will find value using below table.

B. Now as population is normal, sample mean is also normal as per central limit theorem

i. Mean is

ii. Standard deviation is

iii. Distribution is normal as per central limit theorem and shape is bell.

c. Now we need to find

Converting it to z, we get

We have used above table again.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

The cholesterol levels of women aged 21-40 in Canada are approximately Normally distributed with a mean...

The cholesterol levels of women aged 21-40 in Canada are approximately Normally distributed with a mean of 190 miligrams per decilitre (mg/dl). In July of 2007, a clinical assessment applied in Toronto to random sample of twenty–nine Asian female immigrants aged 21-40 had a mean level of 179.52 mg/dl and a standard deviation of 38 mg/dl. (a) At the 10% level of significance test whether the mean cholesterol level of Asian women is the same as the national average. (b)...

The distribution of heights for the population of females in Canada is approximately normally distributed with...

The distribution of heights for the population of females in Canada is approximately normally distributed with a mean of 67.3 inches and a standard deviation of 7 inches. What is the probability that a randomly selected female is shorter than 65 inches? What is the probability that she is between 65 and 70 inches tall? Above what height does one find the tallest 10% of the population? What is the probability that among three females selected at random from the...

Assume that the total cholesterol levels for adults are normally distributed with mean cholesterol level of

Assume that the total cholesterol levels for adults are normally distributed with mean cholesterol level of 51.6 mg/dL and standard deviation14.3 mg/dL. Find the probability that an individual will have a cholesterol level greater than 58 mg/dL.

Assume that the cholesterol levels for adults are normally distributed with mean cholesterol level of 51.5...

Assume that the cholesterol levels for adults are normally distributed with mean cholesterol level of 51.5 mg/dL and standard deviation of 14.3 mg/dL. Find the probability that an individual will have a cholesterol level a.) 60 mg/dL, at least b.) 40 mg/dL, at most c.) Between 40 and 60 mg/dL PLZ show work :)

The distribution of cholesterol levels in a boy is approximately normal with a mean of 170...

The distribution of cholesterol levels in a boy is approximately normal with a mean of 170 and a standard deviation of 30. Levels above 200 require attention. What is the probability of a boy with a cholesterol between 160 and 205?

Assume the cholesterol levels of adult American women are normally distributed with a mean of 190...

Assume the cholesterol levels of adult American women are normally distributed with a mean of 190 mg/dL and a standard deviation of 26 mg/dL. What percent of adult women do you expect to have cholesterol levels of at least 200 mg/dL ? (Round to tenths) b What percent of adult women do you expect to have cholesterol levels between 150 and 170 mg/dL ? (Round to tenths) Above what value are the top 15% of women’s cholesterol levels ?...

The blood cholesterol levels for U.S. adults are normally distributed, with μ = 202 and σ...

The blood cholesterol levels for U.S. adults are normally distributed, with μ = 202 and σ = 41 (units in milligrams per deciliter). A random sample of 60 U.S. adults are chosen and their cholesterol levels are measured. Find P(x⎯⎯⎯ > 210) for n = 60. Enter your answer as an area under the curve with 4 decimal places. P(x⎯⎯⎯ > 210) =

The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a...

The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 223 milligrams per deciliter and a standard deviation of 37.2 milligrams per deciliter.(a) What percent of the men have a total cholesterol level less than 228 milligrams per deciliter of blood?(b) If 251 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 259 milligrams per deciliter of blood?(a)...

1.) Suppose heights of two-year-olds are normally distributed with a mean of 30 inches and a...

1.) Suppose heights of two-year-olds are normally distributed with a mean of 30 inches and a standard deviation of 3.5 inches. a) What is the probability that one two-year-old will be shorter than 28 inches? b) If random samples of size n = 40 two-year-olds are selected, what is the approximate shape, mean, and standard deviation of the sampling distribution of sample means? c) What is the probability that the sample mean of these 40 two-year-olds will be shorter than...

Cholesterol levels for a group of women aged 50-59 follow an approximately normal distribution with mean...

Cholesterol levels for a group of women aged 50-59 follow an approximately normal distribution with mean 216.57 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 29.6% of women fall into this category. 1. What is the Z-score that corresponds to the top 29.6% (or the 70.4-th percentile) of the standard normal distribution? Round your answer to three decimal places. 2. Find the standard deviation of...

Subjects