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The number of books that high school students in the United States read in a year is normally distributed with a mean of 25 books and a standard deviation of 2.5 books. Complete the input for the spreadsheet program to calculate the probability that a high school student chosen at random will read more than 28 books in a year. Then identify this probability. Round the answers to the nearest tenth.

A. Mean
B. Standard deviation
C. X
D. Cumulative
E. = Normdist (B3, B1, B2, B4)

1. _
2. _
3. _
4. True
5._

The probability that a high school student chosen at random will read more than 28 books in a year is _%

1 answer

To calculate the probability that a high school student reads more than 28 books in a year, we will utilize the normal distribution parameters you've provided. Here's how you'd fill in the inputs for the spreadsheet program:

A. Mean (B1): 25 B. Standard deviation (B2): 2.5 C. X (B3): 28 D. Cumulative (B4): True or False (Since we want to calculate P(X > 28), use True for cumulative and then we will subtract from 1 later)

E. The formula syntax should be corrected. Instead of = Normdist (B3, B1, B2, B4) it should be = NORM.DIST(B3, B1, B2, TRUE) (assuming you are using Excel).

Now, let's calculate the probability step by step.

  1. Calculate the cumulative probability using the normal distribution function:

    • P(X ≤ 28) = =NORM.DIST(28, 25, 2.5, TRUE)

    Using the provided mean and standard deviation, you can calculate this value.

  2. Calculate the probability of reading more than 28 books:

    • P(X > 28) = 1 - P(X ≤ 28)

You can calculate P(X ≤ 28) and then subtract it from 1 to get P(X > 28).

Assuming you calculate it using Excel or another statistical tool:

  • Let's say P(X ≤ 28) equals approximately 0.8413 (this value comes from standard normal tables or calculations).

Therefore:

  • P(X > 28) = 1 - P(X ≤ 28)
  • P(X > 28) = 1 - 0.8413 = 0.1587

Now, converting to percentage:
P(X > 28) ≈ 0.1587 * 100 = 15.9%

The final answers are:

  1. 25
  2. 2.5
  3. 28
  4. True
  5. (Use the calculation result from your spreadsheet)

The probability that a high school student chosen at random will read more than 28 books in a year is 15.9%.