47. The lower limit of your range of interest has a z-score of
... z = (x -μ)/σ = (1810 -3550)/870 = -2
The empirical rule tells you 95% of the distribution lies within ±2σ of the mean, so 5% lies in the two tails. Then 2.5% lies in the lower tail of the distribution beyond -2σ.
The upper limit of your range of interest has a z-score of
... z = (4420 -3550)/870 = 1
The empirical rule tells you 68% of the distribution lies within ±1σ of the mean, so 32% lies in the two tails. Then 16% lies in the upper tail beyond +1σ.
The sum of the lower tail and the upper tail beyond your range of interest is
... 2.5% + 16% = 18.5%
Thus the percentage of cars in the weight range of interest is
... 100% - 18.5% = 81.5% . . . . . selection d
48. My calculator says P(x>4000) = 0.30249383... An on-line calculator (shown below) shows the result as 30.25% (in agreement with my calculator). Since one of your selections appears to be 30.42%, we suspect a transposition error somewere along the line. Your best choice is selection b.
