Question

The blood cholesterol levels of men aged 55 to 64 are approximately normally distributed with mean 222 mg/dl and standard deviation 37 mg/dl.

We can estimate that 10% percent of the men aged 55 to 64 have cholesterol level _____ mg/dl or higher. (round to an integer)

Answer 1

It is provided that 10% of the men aged 55 to 64 have cholesterol level 270 mg/dl or higher.

Explanation:

Let X = blood cholesterol levels of men aged 55 to 64 years.

The random variable X follows a Normal distribution with mean μ = 222 mg/dl and standard deviation σ = 37 mg/dl.

It is provided that 10% of the men aged 55 to 64 have cholesterol level x mg/dl or higher.

Compute the value of x as follows:

`P(X\geq x)=0.10\\P((X-\mu)/(\sigma)\geq (x-222)/(37))=0.10\\P(Z\geq z)=0.10\\1-P(Z<z)=0.10\\P(Z<z)=0.90`

Use the z-table to compute the value z for the probability 0.90.

The value of z is 1.29.

Compute the value of x as follows:

`z=(x-\mu)/(\sigma)\\1.29=(x-222)/(37) \\x=222+(1.29*37)\\=269.73\approx270`

Thus, 10% of the men aged 55 to 64 have cholesterol level 270 mg/dl or higher.