Scores on the SAT Mathematics test are believed to be Normally distributed.  The scores of a simple random sample of five students who recently took the exam are 550, 620, 710, 520, and 480.  What is a 80% confidence interval for m, the population mean score on the SAT Math test?

Group of answer choices

(456.7, 695.3)

(463.4, 688.6)

(489.5, 662.5)

(513.8, 638.2)

To calculate the 80% confidence interval for the population mean \( \mu \), we will follow these steps:

### Step 1: Calculate the sample mean

The sample data is:
\[
550, 620, 710, 520, 480
\]

The sample mean \( \bar{x} \) is calculated as:

\[
\bar{x} = \frac{550 + 620 + 710 + 520 + 480}{5} = \frac{2880}{5} = 576
\]

### Step 2: Calculate the sample standard deviation

First, calculate the deviations from the mean, square them, and then find the average of these squared deviations (this is the variance).

\[
\text{Deviation} = x - \bar{x}
\]
\[
\text{Deviations} = 550 - 576, 620 - 576, 710 - 576, 520 - 576, 480 - 576
\]
\[
= -26, 44, 134, -56, -96
\]
Square these deviations:
\[
(-26)^2 = 676, \quad 44^2 = 1936, \quad 134^2 = 17956, \quad (-570^r12 - negativegence would . and teace21 is said

Scores on the SAT Mathematics test are believed to be Normally distributed. The scores of a simple random sample of five students who recently took the exam are 550, 620, 710, 520, and 480. What is a 80% confidence interval for m, the population mean score on the SAT Math test?

Calculate the 80% confidence interval for the population mean of SAT Math scores based on a sample of five students: 550, 620, 710, 520, and 480. This problem uses concepts of normal distribution, confidence intervals, and sample statistics. Suitable for students in Grades 11-12.

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