Homework: Week score: 0 of 2 pts 2.4.31 1 Homework pts 21 of 24 (20 complete) w
ID: 3336598 • Letter: H
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Homework: Week score: 0 of 2 pts 2.4.31 1 Homework pts 21 of 24 (20 complete) w score: 75 8396, 30.33 of Question Help * The mean value of land and buildings per acre from a sample of farms is $1600, with a standard deviation of $300 The data set has a bell-shaped distribution Assume the number of farms in the sample is 79 (a) Use the empiical rule to estimate the number of farms whose land and building values per acre are between S1300 and $1900 54 farms (Round to the nearest whole number as needed) (b) iT 22 additional farms were sampled about how many of these additional farms would you expect to have land and building values between $1300 per acre and $1900 per acre? farms out of 22 (Round to the nearest whole number as needed.) Enter your answer in the ansuter box and then dilck SecknweExplanation / Answer
The mean is $1600. The standard deviation is $300 and the sample size is 79. The emperical rule applies to normal,bell shaped curve and according to it 68% of the data lies within one standard deviation of the mean, 95% of the data lies within two standard deviation of the mean and 99.7% of the data lies within three standard deviation of the mean. In this problem, the mean is $1600 and standard deviation is $300. So, one standard deviation from the mean is ($1600-$300, $1600+$300) i.e $1300 and $1900. So, according to the emperical rule 68% of the data are between $1300 and $1900.
a.) i.e 79*.68= 53.73, or rounded to 54 farms.
b.) If 22 additional farms were sampled, then 68% of the additional farms i.e we would expect that .68*22=14.96, or rounded to 15 farms have land and buildings values between $1300 per acre and $1900 per acre.
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