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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.(2 points) This table outlines statistical analysis calculations, including mean, standard deviation, and cumulative distribution, using the NormDist function. This table represents inputs for the spreadsheet program, requiring values for mean, standard deviation, and x to compute the normal distribution probability. A B 1 Mean 2 Standard Deviation 3 x 4 Cumulative TRUE 5 =NormDist (B3, B1, B2, B4) % The probability that a high school student chosen at random will read more than 28 books in a year is %.

2 answers

To calculate the probability that a high school student chosen at random will read more than 28 books in a year using a normal distribution, you need to follow these steps based on the input you provided:

  1. Fill in the values:

    • Mean (B1): 25
    • Standard Deviation (B2): 2.5
    • x (the value we are interested in, which is 28): B3 = 28

  2. Adjust the formula: Since you want to find the probability of reading more than 28 books, you need to find the cumulative probability for reading 28 books and then subtract that from 1.

    In the cells you've described:

    • Cumulative (B4): TRUE (for cumulative distribution to be True in the original formula, but here we want to utilize FALSE for the exact probability calculation.)

  3. Correct formula for probability greater than 28 books: Since the goal is to calculate P(X > 28), you should use:

    \[ P(X > 28) = 1 - P(X \leq 28) \]

    Hence, the spreadsheet should contain the following formula:

    • For cumulative distribution, it should read:
    =1 - NormDist(B3, B1, B2, TRUE)

  4. Calculate it in a spreadsheet cell:

    • Place the formula in any cell, say cell B5, to compute the result.

  5. Probability Calculation: Using the normal distribution:

    • Mean (µ) = 25
    • Standard Deviation (σ) = 2.5
    • x = 28

Now performing the calculations:

  1. Use the NormDist function:

    • \( P(X \leq 28) = NormDist(28, 25, 2.5, TRUE) \).

  2. Compute \( P(X > 28) = 1 - P(X \leq 28) \).

Using a calculator or spreadsheet, you can find that:

  • \( P(X \leq 28) \approx 0.8413 \) (make sure to find this value from the normal distribution)

Thus:

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

So the percentage of students reading more than 28 books is:

  • 15.9% when rounded to the nearest tenth.

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

what is B5???