select the correct answer.\nthe numbers of beads on 500 handcrafted bead necklaces follow a normal…

select the correct answer.\nthe 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?\na. about 24 necklaces have more than 28 beads.\nb. about 48 necklaces have more than 28 beads.\nc. about 80 necklaces have more than 28 beads.\nd. about 96 necklaces have more than 28 beads.

select the correct answer.\nthe 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?\na. about 24 necklaces have more than 28 beads.\nb. about 48 necklaces have more than 28 beads.\nc. about 80 necklaces have more than 28 beads.\nd. about 96 necklaces have more than 28 beads.

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 28$, $\mu=24$, and $\sigma = 4$. So $z=\frac{28 - 24}{4}=\frac{4}{4}=1$.

Step2: Find the proportion of data above z = 1

Using the standard normal distribution table, the proportion of data to the left of $z = 1$ is approximately $0.8413$. So the proportion of data to the right of $z = 1$ is $1-0.8413 = 0.1587$.

Step3: Calculate the number of necklaces

There are $n = 500$ necklaces. The number of necklaces with more than 28 beads is $n\times0.1587=500\times0.1587 = 79.35\approx80$.

Answer:

C. About 80 necklaces have more than 28 beads.