Question

The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c).

Temperature: 50-59 60-69 70-79 80-89 90-99 100-109

Days: 2 306 1470 1529 311 9

mean = ___________

standard deviation = _______________

(b) Use the frequency histogram of the data to verify that the distribution is bell shaped.

____ No, the frequency histogram of the data is not bell shaped.

____ Yes, the frequency histogram of the data is bell shaped.

(c) According to the empirical rule, 95% of days in the month will be between what two temperatures?

______ and ______

Answer 1

x	f	f*m	f*m2
54.5	2	109	5940.5
64.5	306	19737	1273036.5
74.5	1470	109515	8158867.5
84.5	1529	129200.5	10917442
94.5	311	29389.5	2777307.8
104.5	9	940.5	98282.25
total	3627	288891.5	23230877
mean =x̅=Σf*M/Σf=	79.650
Variance σ2=(ΣfM2-(ΣfM)2/n)/n=			60.82
Std deviation σ=		√σ2 =	7.799

from above:

mean =79.65

standard deviation =7.80

b)

Yes, the frequency histogram of the data is bell shaped.
c)

since from empirical rule, 95% of days are 2 standard deviation from the mean value:

95% interval values = 79.65 -/+ 2*7.80 = 64.05 and 95.25