Question

1.Weights of Old English Sheepdogs are normally distributed with a mean of 63 pounds and a standard deviation of 3 pounds. Using the Empirical Rule, what is the approximate percentage of sheepdogs weighing between 60 and 66 pounds?

2.Pro golf scores are bell-shaped with a mean of 70 strokes and a standard deviation of 4 strokes. Using the empirical rule, in what interval about the mean would you expect to find 99.7% of the scores?

3. Running times in a daily workout have a mean of 36 minutes and a standard deviation of 7 minutes. The distribution is unknown. Using Chebyshev's Rule, in what interval about the mean would you expect to find at least 89% of the workout times?

4. A distribution of tire pressures(psi) has the following 5-number summary. What percentage of data is between 42 and 87 ?

21	42	60	87	108
Min	Q1	Median	Q3	Max

Answer 1

1)

µ =    63          
σ =    3          
we need to calculate probability for ,              
P (   60   < X <   66   )
=P( (60-63)/3 < (X-µ)/σ < (66-63)/3 )              
              
P (    -1.000   < Z <    1.000   )

about 68% of observation of data lie within 1 std dev away from mean

answer: 68%

2)

about 99.7% of observation of data lie within 3 std dev away from mean

±3σ+µ  

X1 =   -3.000   *4+70=   58.00
X2 =   3.000   *4+70=   82.00

interval (58, 82 )

3)

about 89% of observation of data lie within 3 std dev away from mean

±3σ+µ

X1 =   -3.000   *7+36=   15.00
X2 =   3.000   *7+36=   57.00

( 15 , 57 )

4) 50 percentage of data is between 42 and 87