an =A population of values has a normal distribution with y = 218.4 and o = 86.3. A random sample of size167 is drawn. Find the probability that a sample of size n = 167 is randomly selected with a mean lessthan 220.4. Round your answer to four decimal places.PM <220.4)

Respuesta :

Given:

[tex]\mu=218.4,\sigma=86.3.n=167\text{ and M=220.4}[/tex]

The z-score value is

[tex]z=\frac{M-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]

[tex]\text{Substitute }\mu=218.4,\sigma=86.3.n=167\text{ and M=220.4, we get}[/tex]

[tex]z=\frac{220.4-218.4}{\frac{86.3}{\sqrt[]{167}}}[/tex]

[tex]z=\frac{\sqrt[]{167}(220.4-218.4)}{86.3}[/tex]

[tex]z=0.29949[/tex]

The P-value from the z-table is

[tex]P(218.4[tex]P(M<220.4)=0.11772+0.5[/tex]

[tex]P(M<220.4)=0.61772[/tex]

Hence the answer is

[tex]P(M<220.4)=0.61772[/tex]