SOLUTION: Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people. (You may need to use th

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people. (You may need to use th      Log On


   

Question 883064: Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people. (You may need to use the standard normal distribution table. Round your answers to the nearest whole number.)
(a) How many would you expect to be between 170 and 175 cm tall?

(b) How many would you expect to be taller than 176 cm?
Answer by stanbon(75887) About Me  (Show Source):
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Suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. We find the heights of 50 people. (You may need to use the standard normal distribution table. Round your answers to the nearest whole number.)
(a) How many would you expect to be between 170 and 175 cm tall?
z(170) = (170-170)/5 = 0
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z(175) = (175-170)/(5) = 1
P(170<= x <=175) = P(0<= z <= 1) = 0.3413
# expected between 170 and 175 cm is 0.3413*50 = 17.07
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(b) How many would you expect to be taller than 176 cm?
z(176) = (176-170)/(5) = 1/5
P(x > 176) = P(z > 1/5) = normalcdf(1/5,100) = 0.42
# expected is 0.42*50 = 21
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Cheers,
Stan H.
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