The time per week a student uses a lab computer is normally distributed, with a mean of 6.2 hours and a standard deviation of 0.9 hour. A student is randomly selected.

a. Find the probability that a student uses a lab computer less than 4 hours per week.

b. Find the probability that a student uses a lab computer between 5 and 7 hours per week.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores.

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To find the probabilities for a normally distributed variable, we can use the standard normal distribution by converting our values to z-scores.

To do this, we'll use the formula:

z = (x - mean) / standard deviation

Where z is the z-score, x is the value of interest, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.

a. To find the probability that a student uses a lab computer less than 4 hours per week, we need to find the z-score corresponding to 4, and then find the area under the standard normal curve to the left of that z-score.

z = (4 - 6.2) / 0.9 = -2.44

Using a z-table or a calculator, we can find that the area to the left of z = -2.44 is approximately 0.0073.

Therefore, the probability that a student uses a lab computer less than 4 hours per week is approximately 0.0073.

b. To find the probability that a student uses a lab computer between 5 and 7 hours per week, we need to find the z-scores corresponding to 5 and 7, and then find the area under the standard normal curve between those two z-scores.

z1 = (5 - 6.2) / 0.9 = -1.33
z2 = (7 - 6.2) / 0.9 = 0.89

Using a z-table or a calculator, we can find the area to the left of z = -1.33 as approximately 0.0918, and the area to the left of z = 0.89 as approximately 0.8133.

To find the area between these two z-scores, we subtract the smaller area from the larger area:

0.8133 - 0.0918 = 0.7215

Therefore, the probability that a student uses a lab computer between 5 and 7 hours per week is approximately 0.7215.