What percent of women over 20 have upper arm lengths less than 32.9 cm?

Question

The upper arm length of females over 20 years old in a country is approximately Normal with mean 35.1 centimeters (cm) and standard deviation 2.2 cm. Use the 68-95-99.7 rule.

Answer 1

The "trick" of this type of problem is to figure out how many standard deviations the question is asking for.

 

In this case, 32.9 is one standard deviation below the mean.

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From the 68-95-99.7 rule, we have 68% within =/- one standard deviation of 35.1, which means that 16.0%  is below 32.9 and 16% is above 37.3.

 

The probability of being below 32.9 is 16%