Question

One year consumers spent an average of ​$24 on a meal at a resturant. Assume that the amount spent on a resturant meal is normally distributed and that the standard deviation is ​$5 Complete parts​ (a) through​ (c) below

Between what two values will the middle 95% of the amounts of cash spent​ fall?

The middle 95% of the amounts of cash spent will fall between X=$ ​and X=$​

Answer 1

z score corresponding to the middle 95% of the amounts of cash spent​ fall is -1.96(for lower side) and +1.96(for upper side) using the z distribution table

given that mean = 24 and standard deviation = 5

Lower value = mean - (z*sd)

= 24 - (1.96*5)

= 14.2

And upper value = mean + (z*sd)

= 24 + (1.96*5)

= 33.8

So, The middle 95% of the amounts of cash spent will fall between X=$14.2 ​and X=$​33.8 (rounded to 1 decimal)

or

The middle 95% of the amounts of cash spent will fall between X=$14.20 ​and X=$​33.80 (rounded to 2 decimal)