48. Reading Rates The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standar

Question

48. Reading Rates The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. (a) What is the reading speed of a sixth-grader whose reading speed is at the 90th percentile

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Ivy 1 week 2021-09-13T00:45:47+00:00 2 Answers 0

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    0
    2021-09-13T00:46:51+00:00

    Answer: the reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.84 per minute

    Step-by-step explanation:

    Since the the reading speed of sixth-grade students is approximately normal, we would apply the formula for normal distribution which is expressed as

    z = (x – µ)/σ

    Where

    x = reading speed

    µ = mean speed

    σ = standard deviation

    From the information given,

    µ = 125 words per minute

    σ = 24 words per minute

    Looking at the normal distribution table, the z value corresponding to the 90th percentile(0.9), is 1.285

    Therefore,

    1.285 = (x – 125)/24

    24 × 1.285 = x – 125

    30.84 = x – 125

    x = 125 + 30.84

    x = 155.84

    0
    2021-09-13T00:47:32+00:00

    Answer:

    The reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.72 words per minute.

    Step-by-step explanation:

    Problems of normally distributed samples are solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

    Z = \frac{X - \mu}{\sigma}

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

    In this problem, we have that:

    \mu = 125, \sigma = 24

    What is the reading speed of a sixth-grader whose reading speed is at the 90th percentile

    This is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

    Z = \frac{X - \mu}{\sigma}

    1.28 = \frac{X - 125}{24}

    X - 125 = 1.28*24

    X = 155.72

    The reading speed of a sixth-grader whose reading speed is at the 90th percentile is 155.72 words per minute.

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