Finding the range from standard deviation and Gaussian Curve

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Data m=65 cm; d=5 cm and distribution in figure.

  • penguins between 65 cm and 75 cm have probability bistribuited between m and m+2d: than 34%+14%=48%; this match with 48%x3000=1440 penguins
  • probability that the penguin's height is less than 60 cm il express of intervall [- infinite; m-d] than the probability is 2%+14%=16%.
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Updated on July 30, 2022

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  • Admin
    Admin over 1 year

    enter image description hereThe figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.

    Suppose the heights of a population of 3,000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters.

    (a) Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall?

    (b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than 60 centimeters? Give your answer to the nearest 0.05.

    The Above problem is from GRE data interpretation.

    for question (a) will we consider the $10\%$ of the total penguin. From the Gaussian curve how to get the percentage to have the range of the penguin which will be in between 65-75 centimeters?

    For the 2nd question, will iI have to find the numbers of penguin of 60-75 centimeters tall? then the probability theory?

  • user3025403
    user3025403 over 8 years
    According to the GRE guide, the answer is 0.15, not 0.16.