Question

The Museum of Science in Boston has an exhibit in which metal balls drop down a chute, bounce around, and wind up in one of 21 bins. After 1000 balls have dropped, the heights within the bins clearly follow a bell-shaped curve. The standard deviation is 3 bins. About how many balls are in bins 1 through 17? 500 680 950 975

Answer 1

Approximately 950 balls are expected to be in bins 1 through 17, following the Empirical Rule and assuming a bell-shaped distribution.

Step-by-step explanation:

The question is about estimating the number of balls in bins 1 through 17 out of 1000, given that the heights of the balls in the bins follow a bell-shaped curve and have a standard deviation of 3 bins. According to the Empirical Rule, approximately 95 percent of the data is within two standard deviations of the mean for a bell-shaped distribution. If the bins are symmetrically distributed about the mean, bins 1 through 17 would encompass the mean and at least two standard deviations below it, capturing approximately 95 percent of the data. Therefore, we would expect about 950 balls to be in bins 1 through 17 because 95 percent of 1000 balls equals 950.