Question

The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1400 and the standard deviation is $65. 1205 1270 1335 1400 1465 1530 1595 Distribution of Prices What is the approximate percentage of buyers who paid between $1270 and $1400? % What is the approximate percentage of buyers who paid less than $1205? % What is the approximate percentage of buyers who paid between $1335 and $1465? % What is the approximate percentage of buyers who paid between $1205 and $1400? % What is the approximate percentage of buyers who paid between $1335 and $1400? % What is the approximate percentage of buyers who paid more than $1530? %

Answer 1

P(1270 < Y < 1400) = P(1270 - mean < Y - mean < 1400 - mean)
                  = P((1270 - mean)/SD < (Y - mean)/SD < (1400 - mean)/SD)
                  = P((1270 - mean)/SD < Z < (1400 - mean)/SD)
                  = P((1270 - 1400)/65< Z < (1400 - 1400)/65)
                  = P(-2 < Z < 0)
                  = P(Z < 0) - P(Z <-2)
                  = 0.4774=47.74%

P(Y < 1205) = P(Y - mean < 1205 - mean)
                  = P( (Y - mean)/SD < (1205 - mean)/SD
                  = P(Z < (1205 - mean)/SD)
                  = P(Z < (1205 - 1400)/65)
                  = P(Z < -3)
                  = 0.0013=13%

P(1335 < Y < 1465) = P(1335 - mean < Y - mean < 1465 - mean)
                  = P((1335 - mean)/SD < (Y - mean)/SD < (1465 - mean)/SD)
                  = P((1335 - mean)/SD < Z < (1465 - mean)/SD)
                  = P((1335 - 1400)/65< Z < (1465 - 1400)/65)
                  = P(-1 < Z < 1)
                  = P(Z < 1) - P(Z <-1)
                  = 0.6829 =68.29%

P(1205 < Y < 1400) = P(1205 - mean < Y - mean < 1400 - mean)
                  = P((1205 - mean)/SD < (Y - mean)/SD < (1400 - mean)/SD)
                  = P((1205 - mean)/SD < Z < (1400 - mean)/SD)
                  = P((1205 - 1400)/65< Z < (1400 - 1400)/65)
                  = P(-3 < Z < 0)
                  = P(Z < 0) - P(Z <-3)
                  = 0.4988= 49.98%

P(1335 < Y < 1400) = P(1335 - mean < Y - mean < 1400 - mean)
                  = P((1335 - mean)/SD < (Y - mean)/SD < (1400 - mean)/SD)
                  = P((1335 - mean)/SD < Z < (1400 - mean)/SD)
                  = P((1335 - 1400)/65< Z < (1400 - 1400)/65)
                  = P(-1 < Z < 0)
                  = P(Z < 0) - P(Z <-1)
                  = 0.3415=34.15%

P(Y > 1530) = P(Y - mean > 1530 - mean)
                  = P( (Y - mean)/SD > (1530 - mean)/SD
                  = P(Z > (1530 - mean)/SD)
                  = P(Z > (1530 - 1400)/65)
                  = P(Z > 2)
                  = 1 - P(Z <= 2)
                  = 0.0227=2.27%