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Section 5.3: Normal Distributions: Finding Values

Answer the questions about the specified normal distribution.

Q1: The lifetime of ZZZ batteries are normally distributed with a mean of 265 hours and a standard deviation ó of 10 hours. Find the number of hours that represent the the 25th percentile.

A1:
x = µ + zó
= 265 + -0.608 (10)
= 271.08



Q2: Scores on an English placement test are normally distributed with a mean of 36 and standard deviation ó of 6.5. Find the score that marks the top 10%.

Q2:
x = µ + zó
= 36 + -1.208 (6.5)
= 28.15

  • statistics -

    Instead of tables I use this applet

    http://davidmlane.com/hyperstat/z_table.html

    When you say 25 percentile, doesn't that mean that 25% of the date is below?
    Your answer of 271 is above the mean, therefore more than the 50% percentile.

    using the second part , entering 365 for mean, and 10 DV, I entered .25 for "shaded area" and clicked on below to get 358.25

    similarly for your second, doesn't top 10% mean that 90% are below??
    so enter mean=36 sd=10 .9 for shade and click below to get 48.8

    (how could your score of 28.15, which is well below the average of 36 put somebody in the top 10% ?)

  • statistics -

    A survey was conducted to measure the number of hours per week adults spend on home
    computers. In the survey, the number of hours was normally distributed, with a mean of 8
    hours and a standard deviation of 1 hour. A survey participant is randomly selected. Find
    the probability that the hours spent on the home computer by the participant are between
    5.5 and 9.5 hours per week.

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