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    Normal distribution probability - Central Limit Theorem

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    Assume men's weights are normally distributed w/ a mean of 172 lb. and a s.d. of 29lb.

    (a) If one man randomly selected, find the probability his weight is between 166 and 176 lb.

    ( b) If 16 men selected, find the probability that the mean weight is between 166 and 176 lb.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:05 pm ad1c9bdddf
    https://brainmass.com/statistics/central-limit-theorem/normal-distribution-probability-central-limit-theorem-26785

    SOLUTION This solution is FREE courtesy of BrainMass!

    This solution shows how to find the probability of an event related to a normal distribution and how to apply the central limit theorem to find the probability of an event related to a sample mean. Please see the attached Word document for details of how to solve this exercise.
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    Hi- Please explain...
    Assume men's weights are normally distributed w/ a mean of 172 lb. and a s.d. of 29lb.
    If one man randomly selected, find P his weight is between 166 and 176 lb. Answer = .1389
    b) If 16 men selected, find P mean weight between 166 and 176 lb. Answer = .5055

    Recall what the Central Limit Theorem Tells us. It says that if you take a sample of size = n from a population with mean = and standard deviation of , then the sample mean, , is a random variable and has mean = and standard deviation = .
    Solution:

    The Central Limit Theorem helps us differentiate between how to handle X, a single observation taken from a distribution, and , the sample mean of n observations taken from that distribution.

    If a single observation is taken from a Normal distribution with mean = and standard deviation = , you make inferences about X, one observation from that distribution by using .

    If a sample of n observations is taken from that same distribution and you want to make inferences about , the mean of those n observations, by using .

    (a)
    The first question is: Find
    Solve it by finding the Z scores using the distribution of X.

    (b)
    The second question is: Find .
    Solve it by finding the Z scores using the distribution of .

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:05 pm ad1c9bdddf>
    https://brainmass.com/statistics/central-limit-theorem/normal-distribution-probability-central-limit-theorem-26785

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