Question

The newsstand at the corner of Manilla Avenue and GreenTree Rd. in GreenTree sells the daily edition of The Pittsburgh Press. The number of papers sold each day follows a normal probability distribution with a mean of 600 copies and a standard deviation of 15 copies. You want to find the probability of selling more than 625 newspapers on any given day. What is the Excel Command

Answer 1

1 - NORM.DIST(625, 600, 15 ,TRUE)

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In Excel:

We use the norm.dist command.

NORM.DIST(x, mean, standard_dev ,cumulative)

x is the tested value, mean and standard_dev are the mean and the standard deviation, while cumulative we use true to find a probability of a value lower than x, so for a value higher than x, we use:

1 - NORM.DIST(x, mean, standard_dev ,TRUE)

Mean of 600 copies and a standard deviation of 15 copies.

mean = 600, standard_dev = 15

You want to find the probability of selling more than 625 newspapers on any given day.

x = 625

What is the Excel Command

1 - NORM.DIST(625, 600, 15 ,TRUE)