The manager of a night club in Boston stated that 85% of the customers are between the ages of 21 and 27 years. If the age of customers is normally distributed with a mean of 24 years, calculate its standard deviation.

The standard deviation of the age of the customers was of 2.08 years.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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

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 this question:

85% of the customers are between the ages of 21 and 27 years.

Since the normal distribution is symmetric, this means, for example, that 27 is the 50 + (85/2) = 92.5th percentile, that is, when , Z has a pvalue of 0.925. So when . We use this to find

The standard deviation of the age of the customers was of 2.08 years.

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )