Answer :
Answer:
The probability that the average number of hours worked per week is more than 20 hours is 0.00052.
Step-by-step explanation:
We are given that the analysis revealed that students typically work an average of 18.1 hours per week, with a standard deviation of 15.3 hours.
We consider a group of 700 freshmen at a community college.
Let [tex]\bar X[/tex] = sample average number of hours worked per week.
The z score probability distribution for sample average is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population average number of hours per week = 18.1 hours
[tex]\sigma[/tex] = standard deviation = 15.3 hours
n = sample of freshmen = 700
Now, the probability that the average number of hours worked per week is more than 20 hours is given by = P([tex]\bar X[/tex] > 20 hours)
P([tex]\bar X[/tex] > 20 hours) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{20-18.1}{\frac{15.3}{\sqrt{700} } }[/tex] ) = P(Z > 3.28) = 1 - P(Z [tex]\leq[/tex] 3.28)
= 1 - 0.99948 = 0.00052
The above probability is calculated by looking at the value of x = 3.28 in the z table which gives an area of 0.99948.
Therefore, the required probability is 0.00052.