Problema Solution
The Problem
The mean value of land and buildings per acre from a sample of 78 farms in $1800, with a standard deviation of $200. The data set has a normal distribution. Estimate the number of farms whose land building values per acre are between $1600 and $2000.
_____ farms (round to the nearest whole number as needed)
Answer provided by our tutors
Get the Z score for $1600:
Z = (1600-1800)/200 = -1.
Get the z score for 2000:
Z = (2000-1800)/200 = 1.
Find P(Z < 1):
P(Z < 1) = 0.8413.
Find P(Z < -1):
P(Z < -1) = 0.1587
Subtract to get:
P(Z < 1) - P(Z < -1) = P(-1 < Z < 1) = 0.6826
Multiply this percentage by the sample size 78:
78*0.6826 = 53 rounded to the nearest whole number
The answer is: 53 farms.