Question

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 _%

Answer 1

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%**.