# Probability calculation using Z score

Please provide an answer to the questions below, if possible using Excel and show your formulas.

A salesperson goes door-to-door in a residential area to demonstrate the use of a new household appliance to potential customers. She has found from her years of experience that after demonstration, the probability of purchase (long run average) is 0.30. To perform satisfactory on the job, the salesperson needs at least four orders this week.

If she performs 15 demonstrations this week, what is the probability of her being satisfactory?

What is the probability of between 4 and 8 (inclusive) orders?

If the salesperson wants to be at least 90 percent confident of getting satisfactory evaluation in her job this week, how many demonstrations should she perform?

How would your answers to above questions change if the probability of success increases (say by training) to 0.35?

© BrainMass Inc. brainmass.com June 4, 2020, 1:34 am ad1c9bdddfhttps://brainmass.com/statistics/probability/probability-orders-demonstrations-household-appliance-407845

#### Solution Preview

Please provide an answer to the questions below, if possible using Excel and show your formulas

A salesperson goes door-to-door in a residential area to demonstrate the use of a new Household appliance to potential customers. She has found from her years of experience that after demonstration, the probability of purchase (long run average) is 0.30. To perform satisfactory on the job, the salesperson needs at least four orders this week.

Answer

Here we can use binomial distribution to answer the questions. Let X be the number of sales out of n demonstrations. The probability density function of Binomial distribution is given by P(X=x) = .

If she performs 15 demonstrations this week, what is the probability of her being satisfactory?

Here we need P(X≥4) = 1-P(X<4).

The cumulative probability of binomial distribution can be computed using the Excel formula =BINOMDIST(x,n,p,1).

The probability ...

#### Solution Summary

The step by step method for computing probability based on Z score is given in the answer. The probability or orders after demonstration of household appliances are determined.