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2 September, 08:40

The average battery life of 2800 manufactured cell phones is recorded and normally distributed. The mean battery life is 12 hours with a standard deviation of 1.3 hours. Find the number of phones who have a battery life in the 12 to 13.3 range. ∗ * Round your answer to the nearest integer. * *Do not include commas in your answer.

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  1. 2 September, 09:05
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    The number of phones is 956

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - The average battery life of 2800 manufactured cell phones is

    recorded and normally distributed

    ∴ n = 2800

    - The mean battery life is 12 hours

    ∴ μ = 12

    - The standard deviation of 1.3 hours

    ∴ σ = 1.3

    - We need P (12 ≤ x ≤ 13.3) to find the number of phones who

    have a battery life in the 12 to 13.3 range

    ∵ z-score = (x - μ) / σ

    ∵ x = 12, μ = 12, σ = 1.3

    ∴ z = (12 - 12) / 1.3 = 0

    - Use the standard normal distribution table

    ∴ The corresponding area = 0.50000

    ∵ x = 13.3, μ = 12, σ = 1.3

    ∴ z = (13.3 - 12) / 1.3 = 1

    - Use the standard normal distribution table

    ∴ The corresponding area = 0.84134

    ∴ P (12 ≤ z ≤ 13.3) = 0.84134 - 0.50000 = 0.34134

    ∵ P (12 ≤ z ≤ 13.3) = P (12 ≤ x ≤ 13.3)

    ∴ P (12 ≤ x ≤ 13.3) = 0.34134

    ∵ The number of phones is 2800

    ∵ The probability of a battery life in the range 12 to 13.3 is 0.34134

    ∴ The number of phones who have a battery life in this range is

    2800 * 0.34134 = 955.752 ≅ 956 phones

    * The number of phones is 956
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