Question

Sarah makes beaded necklaces to sell at art festivals. The number of beads per necklace follows a normal distribution with a mean of 20 beads and a standard deviation of 5 beads. 95% of the necklaces have what interval of beads?

a) 10 to 30 beads
b) 15 to 25 beads
c) 18 to 22 beads
d) 12 to 28 beads

Answer 1

Option A). The interval of beads for 95% of the necklaces is 10 to 30 beads.

Step-by-step explanation:

With a mean of 20 beads and a standard deviation of 5, the quantity of beads in each necklace is distributed normally. We must ascertain the range that contains the middle 95% of the data in order to calculate the bead interval for 95% of the necklaces.

We can determine that roughly 68% of the data fall within one standard deviation of the mean, 95% fall within two standard deviations, and more than 99% fall within three standard deviations using the Empirical Rule for a normal distribution.

Two standard deviations above and below the mean must be determined in order to compute the interval for 95% of necklaces. 20 - (2 * 5) = 10 beads would be two standard deviations below the mean, and 20 + (2 * 5) = 30 beads would be two standard deviations above the mean. Thus, a) 10 to 30 beads is the correct answer.