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.
[tex]n = 49[/tex]
[tex]\mu = 12[/tex]
[tex]\sigma = 3.5[/tex]
We are supposed to find the probability of selecting a sample mean of 13 or larger from this population i.e.[tex]P(x\geq 13)[/tex]
[tex]Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z=\frac{13-12}{\frac{3.5}{\sqrt{49}}}[/tex]
Z=2
Refer the z table
[tex]P(Z<2)=0.9772[/tex]
[tex]P(x\geq 13)=1-P(Z<2)=1-0.9772=0.0228[/tex]
Hence the probability of selecting a sample mean of 13 or larger from this population is 0.0228
