Question

1. The manager of a bar and grille in Dallas has been gathering data on the number of minutes a  

    party of four spends in the restaurant from the moment they are seated to when they pay the

    check. Round all values to the 4^th decimal place SHOW WORK INCLUDING FORMULA USED

1. Calculate the mean number of minutes (E(x)) for a dinner party of four.
2. What is the variance and standard deviation?

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Number of Minutes   Probability

            x                            P(x)                x P(x)                  x - E(x)                     (x – E(x))² P(x)

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         60                           0.30       

           70                           0.20                                                                                             

           80                           0.15       

           90                           0.35      

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                    E(x) = ∑ [xP(x)] =                                   σ² =∑ [(x – E(x))² P(x)] =

1. E(x) = ∑ [xP(x)] =

2. Variance, σ² =∑ [(x – E(x))² P(x)] =

3. Standard deviation, σ =

Answer 1

a. the mean number of minutes (E(x)) for a dinner party of four is 75.5 minutes.

b. The required variance is 166.75

c. The required standard deviation is 12.9132

The necessary work is done below :