Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 133 pages if the mean is 189 pages and the standard deviation is 28 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.

2.5% probability that a randomly selected book has fewer than 133 pages.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 189 pages

Standard deviation = 28 pages

What is the probability that a randomly selected book has fewer than 133 pages?

133 = 189 - 2*28

So 133 is two standard deviations below the mean.

The Empirical Rule states that 95% of the measures are within 2 standard deviations of the mean. The other 5% is more than two standard deviations distant from the mean. The normal distribution is symmetric, which means that of those 5%, 2.5% are more than 2 standard deviations below the mean and 2.5% are more than 2 standard deviations above the mean.

This means that there is a 2.5% probability that a randomly selected book has fewer than 133 pages.

is there a picture

step-by-step explanation:

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.