fams is $1700, with a standad deviation of $200 The data set has a bell shaped d
ID: 3134554 • Letter: F
Question
fams is $1700, with a standad deviation of $200 The data set has a bell shaped distribution Assume the number of farms in the sample s e is 75 T The mean value of land and buildings per acre from a sample of T Use the onpeical nue to estimate the number of farms whose land and building values per acre are between $1500 and $1900 a) trms pund to the norest whie number as needed) 824 addtond farms wee sampled about how mar y of these additraltams wold you expect tohave land and building values between $1500 per acre and S190 per acre? tarme cout of 24 (Round to the farms odt of 24 (Round to the nearest whole number as needed) e your anwer in each of the answer boxes ELENENTExplanation / Answer
a.
Empirical rule
Given that the mean (u) of a normal probability distribution is 1700 and the
standard deviation (sd) is 200
About 68% of the area under the normal curve is within one standard deviation of the mean. i.e. (u ± 1s.d)
So to the given normal distribution about 68% of the observations lie in between
= [1700 ± 200]
= [ 1700 - 200 , 1700 + 200]
= [ 1500 , 1900 ]
i.e 68% of the farms in the given 75 of whose land and acre are b/w 1500 to 1900
68% of 75 is = 68 * 75/100 = 68*3/4 =51
b.
when additional 24 are sampled,
68% of ( 75 + 24 additionals ) = 99 of whose land and acre are b/w 1500 to 1900
68% of 99 is = 68 * 99/100 = 67.32 ~ 67
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