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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?

A )About 24 necklaces have more than 28 beads.

B )About 48 necklaces have more than 28 beads.

C)About 80 necklaces have more than 28 beads.

D)About 96 necklaces have more than 28 beads.

Respuesta :

The correct answer is C.) About 80 necklaces have more than 28 beads. Have a good day! I hope this has helped.

By converting the data into standard normal distribution, the statement that summarizes the data is: About 80 necklaces have more than 28 beads.

The correct answer is an option (C)

What is standard normal distribution?

"It is a special normal distribution where the mean is 0 and the standard deviation is 1."

What is z-score?

  • "It tells you how many standard deviations from the mean each value lies."
  • "Any normal distribution can be standardized by converting its values into z-scores."

For given question,

We have been given :

Mean = 24 beads

Standard deviation = 4 beads

= P(X >= 28)

= 1 - P(X < 28)

[tex]= 1 - P(\frac{X- mean }{stnadard\ deviation} < \frac{28 - mean}{standard\ deviation} )[/tex]

[tex]= 1 - P(\frac{X - 24}{4} < 1)\\ \\= 1- P(Z < 1)\\\\= 1 - 0.84\\\\= 0.16[/tex]

The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads.

Number of necklaces that have more than 28 beads  

= 0.16 * 500

= 80 (approximately)

By converting the data into standard normal distribution, the statement that summarizes the data is: About 80 necklaces have more than 28 beads.

The correct answer is an option (C)

Learn more about standard normal distribution here

https://brainly.com/question/14916937

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