Which one of the following suggests that the data set is approximately normal? a. A data set with 14, 68, and s41.
b. A data set with 1330, 2940, and s2440.
c. A data set with 2.2, 7.3, and s2.1.
d. A data set with 105, 270, and s33.

a. A data set with 14, 68, and s41.

Step-by-step explanation:

For a normally distributed data set; Q₁ and Q₃ will be 0.6745 × 2 = 1.349 standard deviation.

The interquartile range IQR = Q₃ -  Q₁ = 1.349 ×

              Q₁        Q₃                   IQR = Q₃ -  Q₁             1.349 ×

a.            14        68          41               = 68 - 14              1.349 × 41

                                                            = 54                   = 55.309

b.         1330      2940      2440         = 2940 - 1330      1.349 × 2440

                                                           = 1610                  = 3291.56

c.         2.2         7.3          2.1            = 7.3 - 2.2             1.349 × 2.1

                                                           = 5.1                   = 2.8329

d.         105        270          33           = 270 - 105          1.349  × 33

                                                          = 165                   = 44.517

From the above calculation, we will see that option a have a data set that is approximately normal.