The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?

About 24 necklaces have more than 28 beads.

About 48 necklaces have more than 28 beads.

About 80 necklaces have more than 28 beads.

About 96 necklaces have more than 28 beads.

Question

The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?

About 24 necklaces have more than 28 beads.

About 48 necklaces have more than 28 beads.

About 80 necklaces have more than 28 beads.

About 96 necklaces have more than 28 beads.

debbieg · Answer

28 beads is 1 standard deviation above the mean, so the z-score is 1. 84.13% of the values lie to the left of z=1. Therefore, about 420 of the necklaces of 28 or fewer beads, so about 80 have more than 28 beads.