Question

Blood potassium level, continued. Judy’s measured potassium level varies according to the Normal distribution with with μ=3.8 and σ=0.2mmol/l. Let’s consider what could happen if we took 4 separate measurements from Judy. What is the blood potassium level L such that the probability is only 0.05 that the average of 4 measurements is less than L? (Hint: This requires a backward Normal calculation.)

the book says about 3.64 but i got 3.28

Answer 1

The value of l = 3.64

Explanation:

Consider the provided information.

μ=3.8 and σ=0.2mmol/l and n=4

As we know
`\mu_(\bar x)=\mu=3.8`

`\sigma_(\bar x)=(\sigma)/(√(n))=(0.2)/(√(4))=0.1`

We have given α = 0.05

So by the standard normal table:
`Z_(0.05)=-1.645`

Compute
`P(\bar{X}<l)=0.05`

`P(z<(l-3.8)/(0.1))=0.05`

`(l-3.8)/(0.1)=-1.645`

`l-3.8=-0.1645`

`l=3.64`

Hence, the value of l = 3.64