The number of hours per week that high school students spend on homework is normally distributed,with a mean of 12 hours and a standard deviation of 3 hours.50 students are chosen at random.Let
Represent the mean number of hours spent on homework for this group.Find the probability that
Is between 10.8 and 13.0.
A)0.0078
B)0.286
C)0.9886
D)0.4711
E)0.0143

Question

The number of hours per week that high school students spend on homework is normally distributed,with a mean of 12 hours and a standard deviation of 3 hours.50 students are chosen at random.Let 
Represent the mean number of hours spent on homework for this group.Find the probability that 
Is between 10.8 and 13.0.
A)0.0078 
B)0.286 
C)0.9886 
D)0.4711 
E)0.0143

Quizplus · Accepted Answer

We know that the distribution of the mean number of hours spent on homework follows a normal distribution with mean μ = 12 and standard deviation σ/√n = 3/√50 ≈ 0.4243.

To find the probability that the mean number of hours is between 10.8 and 13.0, we need to standardize these values:

z1 = (10.8 - 12) / 0.4243 ≈ -3.3842
z2 = (13 - 12) / 0.4243 ≈ 2.3591

Using a standard normal distribution table or calculator, we find the probability that z is between -3.3842 and 2.3591 is approximately 0.9886.

Therefore, the answer is choice C (0.9886).

The Number of Hours Per Week That High School Students