Suppose that people's heights ( in cm) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people.
a). How many would you expect to be between 170 and 180 cm?
b). How many would you expect to be taller than 176 cm?
a). How many would you expect to be between 170 and 180 cm?
b). How many would you expect to be taller than 176 cm?
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z = (x - mu) / sigma ---> mu = mean = 170 sigma = sd = 5
a) calculated:
upper: z = (180 - 170) / 5 = 2 ----> look up p(z=2) = 0.9722
lower: z = (170-170) / 5 = 0 ----> look up p(z=0) = 0.5000
difference 0.9722 - 0.5000 = 0.4722 = probability
Expected = np = 50 (0.4722) = 23.61 ---> 24 people
another way to do this is to look at the normal distribution... you're looking at a range of 10 (2 times standard deviation) and you know the probability for +1/+2 sd ~48%
b) for the area taller than 176 ---> 1-p(<=176)
z = (176-170)/5 = 1.2
p(z=1.2) = 0.8849
because you want the area above 176, 1-0.8849=0.1151
Expected value = np = 50(0.1151) = 5.755 = 6 people
a) calculated:
upper: z = (180 - 170) / 5 = 2 ----> look up p(z=2) = 0.9722
lower: z = (170-170) / 5 = 0 ----> look up p(z=0) = 0.5000
difference 0.9722 - 0.5000 = 0.4722 = probability
Expected = np = 50 (0.4722) = 23.61 ---> 24 people
another way to do this is to look at the normal distribution... you're looking at a range of 10 (2 times standard deviation) and you know the probability for +1/+2 sd ~48%
b) for the area taller than 176 ---> 1-p(<=176)
z = (176-170)/5 = 1.2
p(z=1.2) = 0.8849
because you want the area above 176, 1-0.8849=0.1151
Expected value = np = 50(0.1151) = 5.755 = 6 people