Probability

[newbiestats]

Being asked to recall some simple probability, here's one I am doing and can't remember much, could somebody help please

1. CNAE, an all-news AM radio station, ?nds that the distribution of the lengths of time listeners are tuned
to the station follows normal distribution with mean 15 minutes and standard deviation 3.5 minutes.
What is the probability that a particular listener will tune in:

(a) for more than 20 minutes?
(b) for 20 minutes or less?
(c) between 10 to 12 minutes?

 

[arthur ohlsten]

mean=15minutes
sigma=3.5 minutes

a)
more than 20 minutes?
20-15=5
how many sigmas?
x=5/3.5
x= 1 and 1.5/3.5
x=1 3/7 sigmas

hrom a table see what the probability is from the mean+ 1 3/7 sigmas to infinity
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b)
for 20 minutes or less
look up in thr table from -infinity to mean + 1 3/7 sigmas.
Or 1 minus the answer found in a).
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between 10 to 12 minutes
10 is 5/3.5 sigmas below the mean
12 is 3/3.5 sigmas below the mean

look up the area from - infinity to mean + 5 /3.5 sigma and subtract the area from - infinity to mean + 3/3.5 sigma
this is identical to determineing the value below the mean due to the symmetry of the normal distribution.
please check the math.
Arthur