Question

Tyus Nedd found that the average cost of automobile collision repairs is $ 3000.29 with a stdev = 53.92. find the range of values in which at least 64.78% of the data will lie. ( you do not need all of the data scores). To get credit, please be accurate to 2 decimal places---do not round prior to arriving at the final answer. Hint: this is a harder version of # 34 on Page 153.

Answer 1

Approximation of the data to Normal distribution (As it is the best way to find the range as per the given data)

Mean cost, u = $3000.29

Stdev, s = 53.92

For 64.78% of the data, from normal distribution curve and z-table

The Z values range from -0.93 to 0.93

Let X denote the cost of automobile repair

For Z = -0.93, X = u - 0.93s = 3000.29 - (0.93*53.92) = 2950.14

And for Z = 0.93, X = u + 0.93s = 3000.29 + (0.93*53.92) = 3050.44

Thus, the required range of values = { 2950.14, 3050.44}