Question

I do not understand the emirical rule. Can someone please explain it by using this equation?

Give an exact answer based on the empirical rule for the question given below.

The price paid for a particular model of HD television is approximately a normal distribution. The mean price paid is $1400 and the standard deviation is $135.

What is the approximate percentage of buyers who paid above $1,805?

What is the approximate percentage of buyers who paid between $1400 and $1,805?

Answer 1

1400 + 3 * 135 = 1805

According to emperical rule about 99.7% of the data falls within 3 standard deviation from the mean.

1805 is 3 standard deviation above the mean.

So 49.85% of the data fall above 3 standard deviation from the mean.

50% - 49.85% = 0.15%

So 0.15% of buyers paid above $ 1805.

b) 1805 is 3 standard deviation above the mean.

According to emperical rule about 99.7% of the data falls within 3 standard deviation from the mean.

49.85% of the data fall above 3 standard deviation from the mean.

So 49.85% of buyers paid between $1400 and $1805.