Question

days probability
1 0.243
2 0.102
3 0.101
4.123
5.133
6.114
7.07
8.046
9.019
10.013
11.01
12 0.008
13 0.006
14 0.004
15 0.004
16 0.002
17 0.001
18 0.001
a) state the random variable.
select an answer
b) if you were to make the corresponding histogram for this frequency table, what shape would the histogram be?
select an answer
c) find the mean number of days to fix defects.
put the numeric answer rounded to 3 decimal places in the first box and the correct units in the second box.
which of the following is the correct symbol for the mean of a probability distribution?

Explanation:

Step1: Define random variable

The random variable \(X\) is the number of days to fix defects.

Step2: Analyze histogram shape

As the probabilities decrease as the number of days increases, the histogram would be left - skewed.

Step3: Calculate the mean

The formula for the mean \(\mu\) of a discrete probability distribution is \(\mu=\sum_{x}x\cdot P(x)\).

$$
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The symbol for the mean of a probability distribution is \(\mu\).

Answer:

a) The random variable \(X\) is the number of days to fix defects.
b) Left - skewed
c) 4.437 days; \(\mu\)