The heart rates for puppies are normally distributed, with a mean heart rate of 180 beats per minute (60-160 beats per minute for most adult dogs) with a standard deviation of 6 bpm (beats per minute). a. what percentage of puppies will have heart rates of less than 187 bpm? b. what percentage of puppies will have heart rates between 170 bpm and 187 bpm? c. if 500 puppies are examined, how many would you expect to have a heart rate of less than 187 bpm? d. 10% of all puppies will have a heart rate greater than what value?

So if the standard deviation is 6 bpm, and the mean = 180, then +1s = 186, +2s = 192, -1s = 174, -2s = 168

a. The % less than 187 are all, including and less than, +1s. So 50% + 34.1% (1s) = 84.1% of the puppies

b. The % between 170 and 187 would be between -1.5s and +1s. So (34.1% × 2) + (13.6/2) = 68.2% + 6.8% = 75% of the puppies

c. Since in a) we said that the % for less than 187 bpm was 84.1%, we just take that % of 500: .841×500 = 420.5, so we'd expect between 420 and 421 puppies

d. 10% of all.puppies will have a heart rate greater than? This is asking what deviation above the mean corresponds to 10%.
This will be around those above around +1.5s, so around 188 bpm

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