suppose the number of customer complaints per day on the morning shift (6am-12) at Murph's Coffee is distributed as follows:

Complaints f(x)
0 .3
1 ???
2 .2

a) what is the value of ???

b)what is the average number of complaints per day on the morning shift?

c)what is the standard deviation of the number of complaints per day on the morning shift?

d)if Y is the number of inexperienced staff people at Murph's on the morning shift, would the values of X and Y be correlated? explain

To answer the given questions, we first need to understand the probability distribution represented by the table.

The table shows the probability distribution of the number of customer complaints per day on the morning shift at Murph's Coffee. The random variable is denoted by X, and the possible values it can take are 0, 1, and 2.

Let's calculate the missing value now:

a) Since the probabilities for all possible values should add up to 1, we can calculate the missing value by subtracting the sum of the probabilities of the other values from 1:

1 - (0.3 + 0.2) = 0.5

So, the missing value is 0.5.

b) To find the average number of complaints per day on the morning shift, we need to calculate the expected value or the mean. It can be calculated by summing the product of each value and its corresponding probability:

Average = (0 * 0.3) + (1 * 0.5) + (2 * 0.2) = 0 + 0.5 + 0.4 = 0.9

The average number of complaints per day on the morning shift is 0.9.

c) The standard deviation of the number of complaints per day on the morning shift can be calculated using the following formula:

Standard Deviation = sqrt(∑(x - μ)^2 * P(x))

Where:
x represents each possible value
μ represents the mean (calculated in part b)
P(x) represents the corresponding probability for each value

Standard Deviation = sqrt((0 - 0.9)^2 * 0.3 + (1 - 0.9)^2 * 0.5 + (2 - 0.9)^2 * 0.2)

Calculating further:

Standard Deviation = sqrt(0.81 * 0.3 + 0.01 * 0.5 + 1.21 * 0.2)
Standard Deviation = sqrt(0.243 + 0.005 + 0.242)
Standard Deviation ≈ sqrt(0.49)
Standard Deviation ≈ 0.7

The standard deviation of the number of complaints per day on the morning shift is approximately 0.7.

d) To determine whether the values of X (number of customer complaints) and Y (number of inexperienced staff people) are correlated, we would need to have information about the relationship between the two variables. Without this information, it is not possible to conclude whether X and Y are correlated or not. Correlation analysis requires measuring the strength and direction of the relationship based on data.