The average spending at Neco’s salad bar is $8.22 with a standard deviation of $2. The distribution follows Normal distribution.

The average spending at Neco’s salad bar is $8.22 with a standard deviation of $2.53. The distribution follows Normal distribution. The management is interested in the middle 85% of the customers (spending wise) as it believes that they represent the customer base. What will be the difference between the upper and lower spending cut-offs which define the middle 85% of the customers?

Selected Answer:7.0864

Got this wrong. I used M+/-z*sigma.

UL=8.22+1.44(2.53)=11.8632

LL+8.22-3.6432=4.75768

The difference is 7.0864, but I got it wrong.

Can you help me understand where I went wrong on my approach?