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: 5 303 1450 1516 438 8

(a) Approximate the mean and standard deviation for temperature.

Mean = __________ (Round to one decimal place as needed.)

Standard Deviation = ___________ (Round to one decimal place as needed.)

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

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

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

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

_____ and _____ (Round to one decimal place as needed. Use ascending order.)

Answer 1

x	f	f*M	f*M2
54.5	5	272.5	14851.25
64.5	303	19543.5	1260555.75
74.5	1450	108025	8047862.5
84.5	1516	128102	10824619
94.5	438	41391	3911449.5
104.5	8	836	87362
total	3720	298170	24146700
mean =x̅=Σf*M/Σf=	80.1532
Variance σ2=(ΣfM2-(ΣfM)2/n)/n=	66.5087799
Std deviation σ=		√σ2 =	8.15529153

• from above mean =80.2

  standard deviation  σ=8.2

b) histogram

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?

95% of days in

-/+ 2*σ =(80.2 -2*8.2 , 80.2 + 2*8.2) = (63.8 , 96.6)

95% of days in the month will be between (63.8 , 96.6)

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