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17 February, 00:17

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)

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  1. 17 February, 00:33
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    Between US$ 109,720 and US$ 180,280 95% of the houses fall

    Step-by-step 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
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