Question 137088: Suppose the terminal velocity of a particular type of projectile is known to be distributed normally with mean 65 mph and standard deviation 2 mph.
If you select a projectile at random, what is the probanility that its terminal velocity will be between 63 & 67 mph?
What is the distribution of the sample mean terminal velocity for samples of size 50 projectiles?
For a sample of 50 projectiles chosen at random, what is the probability that the mean terminal velocity is between 63 & 67 mph?
If we dont know the distribution of the terminal velocity of a particular type of projectile. But we do know that its mean is 65 mph and its standard deviation is 2 mph. Can we still do the questions above?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose the terminal velocity of a particular type of projectile is known to be distributed normally with mean 65 mph and standard deviation 2 mph.
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If you select a projectile at random, what is the probanility that its terminal velocity will be between 63 & 67 mph?
Find the z-scores of 63 and 67
z(63) = (63-65)/2 = -1 ; z(67)=(67-65)/2 = 1
P(63 < x < 67) = P(-1 < z < 1) = 0.6827
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What is the distribution of the sample mean terminal velocity for samples of size 50 projectiles?
mean of the sample means = 65
std of the sample means = 65/sqrt(65)
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For a sample of 50 projectiles chosen at random, what is the probability that the mean terminal velocity is between 63 & 67 mph?
z(63) = (63-65)/[-2/sqrt(50)] = -sqrt50 = -7.07
z(67) = (67-65)/[2/sqrt(50)] = sqrt50 = 7.07
P(63 < x-hat < 67) = P(-7.07 < z < 7.07) is approximately 1
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If we dont know the distribution of the terminal velocity of a particular type of projectile. But we do know that its mean is 65 mph and its standard deviation is 2 mph. Can we still do the questions above?
Another confusing question.
If you know the mean and standard deviation of the terminal valocity
you DO know the distribution. Those two parameters define the distribution.
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Cheers,
Stan H.
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