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 $\overline{ y}$ represent the mean number of hours spent on homework for this group.Find the probability that $\overline{ y}$ is between 10.8 and 13.0.
A)0.0078
B)0.286
C)0.9886
D)0.4711
E)0.0143

Question

Quizplus · Accepted Answer

To find the probability that 11ea9518_d60d_970d_9016_1b403e4fe8a4_TB3450_11 is between 10.8 and 13.0, we need to standardize the values and then find the area under the standard normal distribution curve between those values.

The standardized value for 10.8 is:

z = (10.8 - 12) / 3 = -0.4

The standardized value for 13.0 is:

z = (13.0 - 12) / 3 = 0.333

Using a standard normal distribution table or calculator, we can find the area under the curve between -0.4 and 0.333. This is approximately 0.9886.

Therefore, the probability that 11ea9518_d60d_970d_9016_1b403e4fe8a4_TB3450_11 is between 10.8 and 13.0 is 0.9886.

The closest answer choice is C.

The Number of Hours Per Week That High School Students y‾\overline{ y}y​

The Number of Hours Per Week That High School Students $\overline{ y}$