To start, find the difference between the mean score and the given score.
81.5 %
Practice makes perfect
We have been told that the scores on a test are normally distributed with a mean of 74 and a standard deviation of 8. We will find the probability that a randomly chosen junior has a score between 66 and 90.
66≤ x≤ 90
First, let's find the difference between the mean and 66.
74- 66= 8Then, we will divide the difference by the standard deviation.
8/8=1
Thus, 66 is 1 standard deviation below the mean.
Now let's do the same with 90. Start with finding the difference between this number and the mean.
90- 74=16
Next, divide this difference by the standard deviation.
16/8=2
Thus, 90 is 2 standard deviations above the mean. To find the probability, we will shade the percent of data which is no more than 1 standard deviation below the mean and no more than 2 standard deviations above the mean.
Finally, we can find the probability of choosing a junior with a score between 66 and 90 by adding the probabilities of the shaded areas.
