Question

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean of 13 or larger from this population

Answer 1

The probability of selecting a sample mean of 13 or larger from this population is 0.0228

Explanation:

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.

`n = 49`

`\mu = 12`

`\sigma = 3.5`

We are supposed to find the probability of selecting a sample mean of 13 or larger from this population i.e.
`P(x\geq 13)`

`Z=(x-\mu)/((\sigma)/(√(n)))`

`Z=(13-12)/((3.5)/(√(49)))`

Z=2

Refer the z table

`P(Z<2)=0.9772`

`P(x\geq 13)=1-P(Z<2)=1-0.9772=0.0228`

Hence the probability of selecting a sample mean of 13 or larger from this population is 0.0228