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

Answer:

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

Step-by-step 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.$P(x\geq 13)$

$Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{13-12}{\frac{3.5}{\sqrt{49}}}$

Z=2

Refer the z table

$P(Z$

$P(x\geq 13)=1-P(Z$

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