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22 September, 15:02

Use technology or a z distribution table to find the indicated area The masses of eggs collected on a farm are normally distrobuted with a mean of 55 grams and a standard deviation of 4. w grams approximately 80% of the eggs on the farm have a mass greater than which mass

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  1. 22 September, 15:05
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    This question is incomplete because it was not correctly written and it lacked the appropriate options.

    Complete Question:

    Use technology or a z-distribution table to find the indicated area. The masses of the eggs collected on a farm are normally distributed with a mean of 55 grams and a standard deviation of 4.2 grams. Approximately 80% of the eggs on the farm have a mass greater than which mass?

    a) 51.5 g

    b) 54.1 g

    c) 55.8 g

    d) 58.5 g

    Answer:

    d) 58.5 g

    Step-by-step explanation:

    Using the z score formula

    z = (x-μ) / σ,

    where x is the raw score

    μ is the population mean

    σ is the population standard deviation.

    From the question:

    x is the raw score is unknown

    μ is the population mean = 55 grams

    σ is the population standard deviation = 4.2 grams

    Where were not given the z score but we were given the probability of the z score to be approximately 80%

    Converting 80% to decimal, = 0.80

    P (x
    Using a normal distribution table, the z score corresponding to 0.80 = 0.8416

    Since we have our value for z, we substitute to find x

    z = (x-μ) / σ,

    0.8416 = (x - 55) / 4.2

    0.8416 * 4.2 = x - 55

    (0.8416 * 4.2) + 55 = x

    x = 58.53472

    Approximately = 58.5 grams

    Therefore, approximately 80% of the eggs on the farm have a mass greater than 58.5grams.
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