Question

The mean price of new homes from a sample of houses is $145,000 with a standard deviation of $18,000. The data set has a bell-shaped distribution. Between what two pieces do 95% of the houses fall? (Write answer as lower value and upper value)

Answer 1

Between US$ 109,720 and US$ 180,280 95% of the houses fall

Explanation:

1. Let's review the information given to us to answer the question correctly:

Mean price of new homes from a sample of houses = $145,000

Standard deviation from the sample of houses = $ 18,000

Distribution = Normal or bell-shaped

2. Between what two prices do 95% of the houses fall? (Write answer as lower value and upper value)

For answering the question, we will use the z-table, this way:

Lower value = P = 0.025

Upper value = P = 0.975

Confidence interval = Upper value - Lower value

Confidence interval = 0.975 - 0.025 = 0.95

z-value at p-value (0.025) = − 1.96

z-value at p-value (0.975) = + 1.96

1.96 Standard deviation from the sample of houses = $ 18,000 * 1.96 = 35,280

Lower value = 145,000 - 35,280 = 109,720

Upper value = 145,000 + 35,280 = 180,280

Between US$ 109,720 and US$ 180,280 95% of the houses fall