Answer:
The probability that for the second sample of 500 college students, the mean number of hours worked will be less than 14.6 is 0.6554
Step-by-step explanation:
The sampling distribution of the sample mean is given by a normal distribution with mean [tex]\mu[/tex] and variance [tex]\frac{\sigma^2}{n}[/tex], where [tex]\mu[/tex] is the mean and [tex]\sigma^2[/tex] is the variance of the population that generates the data. In this way the random variable;
[tex]Z=\frac{\bar x - \mu_{\bar x}}{\sigma_{\bar x}}[/tex] is a standard normal variable. As [tex]\bar {x}-\mu_{\bar x} = 0.4\sigma_{\bar x}[/tex], then [tex]Z = 0.4[/tex].
[tex]P (X <14.6) = P (Z <0.4) = 0.6554[/tex]
