An airline computes capacity and range for its planes by assuming the distributi

Question

An airline computes capacity and range for its planes by assuming the distribution of adult passenger weights is a bell-shaped symmetric curve with a mean of 150 lbs and a standard deviation of 20 lbs. Use the z-score to find how many standard deviations away from the mean are the following adult passenger weights are: more than 130 lbs less than 170 lbs Using the empirical rule what proportion of adult passenger weights exceed 170 lbs Using the empirical rule what proportion of adult passenger weights are between 130 and 170 lbs The empirical/long-run probability interpretation says: the probability of any outcome of a random phenomenon can be defined as the proportion of times the outcome would occur in a large series of repetitions. Find a coin, in each part a, b, c calculate the proportion of times you got a tail. Flip coin once flip 5 times flip it 15 times On y-axis the proportion of times you observed tails, on x-axis the number of times you Hipped the coin. If you flipped it 10,000 times, plot the point on the graph that you expect to sec using the empirical/long-run probability interpretation. You don't actually need to flip it 10,000 times just apply the law of large numbers.

Explanation / Answer

1) mean = 150

std dev = 20

a)

For x = 130, the z-value z = (130 - 150) /20 = -1

Hence P(x > 130) = P(z > -1) =1 - [area to the left of -1] = 0.8413

b)

For x = 170, the z-value z = (170 - 150) / 20 = 1

Hence P(x < 170) = P(z <1) = [area to the left of 1] = 0.8413

c)p(x>170) = 1- p(x<170) = 1-0.8413 = 0.1587 = 15.87%

d)P(130<X<170) = P( -1<Z<1) = 0.8413 - 0.1587 = 0.6826 = 68.26%

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