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Statistics help?
An airline has room for 262 passengers on its next flight to New York from Chicago. Because some people do not show up, the airline books 290 people on the flight. If the mean number of "no shows" is 45 people with a std. deviation of 10, what percentage of these flights will be unable to seat all passengers who do show up?
we need to find the probability that fewer than (290 - 262) = 28 no shows come to flight.
For any normal random variable X with mean μ and standard deviation σ , X ~ Normal( μ , σ ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( μ , σ² ). Most software denotes the normal with just the standard deviation.)
You can translate into standard normal units by:
Z = ( X - μ ) / σ
Moving from the standard normal back to the original distribuiton using:
X = μ + Z * σ
Where Z ~ Normal( μ = 0, σ = 1). You can then use the standard normal cdf tables to get probabilities.
If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem.
If a sample of size is is drawn from a population with mean μ and standard deviation σ then the sample average xBar is normally distributed
with mean μ and standard deviation σ /√(n)
An applet for finding the values
http://www-stat.stanford.edu/~naras/jsm/FindProbability.html
calculator
http://stattrek.com/Tables/normal.aspx
how to read the tables
http://rlbroderson.tripod.com/statistics/norm_prob_dist_ed9.html
In this question we have
X ~ Normal( μx = 45 , σx² = 100 )
X ~ Normal( μx = 45 , σx = 10 )
Find P( X < 28 )
P( ( X - μ ) / σ < ( 28 - 45 ) / 10 )
= P( Z < -1.7 )
= 0.04456546
4.45% of the time the flight will not have enough seats for all the people who show up.
Belt CP std forward flight