Standard Deviation, can someone please help me?

Question

 

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). Round all z-scores and percents to the nearest hundredth. Round all probabilities to the nearest ten-thousandths. You must use the z-table provided on pages 2 and 3 of the formula sheet for the Statistics Unit. For any other rounding consider the context of the question.

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?

Answer 1

I am giving you answers that I obtained through use of the TI-83 DISTR menu, using commands for Normal Distribution.

 

a) 87.83%

b) 83.05%

c) 439

d) 187.7

 

Commands:

a) normalcdf(-9999,187,180,6)  <---x scores between -9999 & 187, where mean = 180, s.d. = 6

b) normalcdf(170,187,180,6)

c) 500 times 0.8783

d) invnorm(0.9) = 1.28155 <----Z score for 90% of puppies having heart rate up to some limit; to find what this breakpoint is, Z = 1.28155 = (x - 180)/6) ⇒ x = heart rate 187.7, so 10% will have heart rate exceeding this value.

 

You, having the referenced tables, should get the same answers.  I offer this as a vehicle you can check against. Let me know if you have any questions.