Question

The mean length of Beethoven’s nine symphonies is 37 minutes; the standard deviation is 12 minutes..
All of the following data values lie within how many standard deviations of the mean?
27 min, 30 min, 47 min, 35 min, 30 min, 40 min, 35 min, 22 min, 65 min


a.
1 standard deviation
c.
3 standard deviations
b.
2 standard deviations
d.
4 standard deviations

Answer 1

Mean is 37 and standard deviation is 12.
Mean + 1 standard deviation = 37 + 12 = 49
Mean - 1 standard deviation = 37 - 12 = 25

See if all the data values fall between 25 and 49.
If not, try: mean - 2 standard deviations to mean + 2 standard deviations
Check if all data values lie within. If not try 3 standard deviations until you find the answer.

Answer 2

would it be 3 standard deviations?

Answer 3

Yes.

Answer 4

thank you!

Answer 5

you are welcome.

Answer 6

how about this one? A set of data has mean 62 and standard deviation 4. Find the z-score of the value 78.
a.
16
b.
1.2
c.
–4
d.
4

Answer 7

\[Z = \frac{ X - \mu }{ \sigma } \]

Answer 8

X = 78, mu = Mean = 62, sigma = standard deviation = 4, Z is Z score.

Answer 9

4

Answer 10

Yes.