Question

A survey by Walmart found that people spend on average $26 on each walk-in shopping. Assume the standard deviation is $4.

1. a) Find the z-score of spending $31.8 ?

2. b) Find P(X > 27) using the first method (Z-score table). Interpret the result.

3. c) Find P(X > 27) using the second method (TI 83/84 calculator).
   Show all work by drawing the interval on the Normal Distribution curve and indicating the lower and upper values.

4. d) Find the percentage of people who spend from 19 to 30 dollars Use the first method (Z-score table).

5. e) Find the percentage of people who spend from 19 to 30 dollars.
   Use the second method (TI 83/84 calculator). Show all work by drawing the interval on the Normal Distribution curve and indicating the lower and upper values.

Answer 1

Z-score table-

Z-score table is available online and in the index of books and pdfs from where we can obtain probability directly of our standard normal variable.

TI 83/84 calculator-

In this calculator, we can calculate probability of normal variable (therefor standard normal variable is not mandatory).

The command to be used is as follows.

normalcdf(lower bound, upper bound, mean, standard deviation)

(a)

We can obtain z-score using the transformation

(b)

Required interval is as follows.

Required probability is given by

(c)

Required interval is as follows.

Required probability is given by

Basically upper limit is . But we know 99.73% data is contained in 3 standard deviation internal. So, any value above mean + 3*standard deviation can serve our purpose.

(d)

Required interval is as follows.

Required probability is given by

(e)

Required interval is as follows.

Required probability is given by