An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 90 and a standard deviati

Question

An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 90 and a standard deviation of 12. Use StatCrunch to find the proportion of children have an index of at least 110.

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1 week 2021-11-23T23:23:35+00:00 1 Answer 0 views 0

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  1. Charlotte
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    2021-11-23T23:25:03+00:00

    Answer:

    The proportion of children that have an index of at least 110 is 0.0478.

    Step-by-step explanation:

    The given distribution has a mean of 90 and a standard deviation of 12.

    Therefore mean, \mu = 90 and standard deviation, \sigma = 12.

    It is given to find the proportion of children having an index of at least 110.

    We can take the variable to be analysed to be x = 110.

    Therefore we have to find p(x < 110), which is left tailed.

    Using the formula for z which is p( Z < \frac{x - \mu}{\sigma}) we get p(Z < \frac{110 - 90}{12} = 1.67).

    So we have to find p(Z ≥ 1.67) = 1 – p(Z < 1.67)

    Using the Z – table we can calculate p(Z < 1.67)  = 0.9522.

    Therefore p(Z ≥ 1.67) = 1 – 0.9522 = 0.0478

    Therefore the proportion of children that have an index of at least 110 is 0.0478

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