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.\nwhich 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.\nwhich 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). [ z=\frac{28 - 24}{4}=\frac{4}{4}=1 ]

Step2: Use the empirical rule

The empirical rule for a normal distribution states that about (68%) of the data lies within (z=- 1) and (z = 1), about (95%) lies within (z=-2) and (z = 2), and about (99.7%) lies within (z=-3) and (z = 3). The proportion of data to the right of (z = 1) is (\frac{100%-68%}{2}=16%)

Step3: Calculate the number of necklaces

If there are (n = 500) necklaces, the number of necklaces with more than (28) beads (corresponding to (z>1)) is (n\times0.16) [ 500\times0.16 = 80 ]

Answer:

C. About 80 necklaces have more than 28 beads.