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.
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.
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.
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.