Respuesta :
Answer:
The probability that the selected 25 scores have a mean between 1550 and 1575 will be 0.0316
Step-by-step explanation:
The population has a Mean[tex](\mu)[/tex] of 1518 and standard deviation[tex](\sigma)[/tex] of 325.
Formula for finding z-score is: [tex]z=\frac{X-\mu}{\sigma}[/tex]
So, the z-scores for the mean between 1550 and 1575 are......
[tex]z(X>1550)=\frac{1550-1518}{325} \approx 0.10[/tex]
[tex]z(X<1575)=\frac{1575-1518}{325} \approx 0.18[/tex]
According to the standard normal distribution table: [tex]P(Z<0.10)=0.5398[/tex] and [tex]P(Z<0.18)= 0.5714[/tex]
Now,
[tex]P(1550<X<1575)\\ \\ =P(Z<0.18)-P(Z<0.10)\\ \\ =0.5714-0.5398\\ \\ =0.0316[/tex]
So, the probability that the selected 25 scores have a mean between 1550 and 1575 will be 0.0316
