I believe the answer is 0.1
Answer:
Expected value = 190
Variance = 4000
Step-by-step explanation:
Let X be the number of the trials until the third success of the bad pump.
This implies that X is a negative binomial distribution
having θ = 20% = 0.2.
Now, if for example it will take X trials to use up the three pumps, then the total time is 10 min/trials + extra 10 minutes for the 3 bad pumps
This means the total time is written as;
T = 10X + (10 + 10 + 20)
T = 10X + 40
Mean which is also expected value of X is;
μ_x = 3/0.2 = 15
Variance of X is; σ²_x = 40
Thus;
Mean of T will be;
μ_T = 10μ_x + 40
μ_T = 10(15) + 40
μ_T = 190
Also, variance of T will be;
σ²_T = 10²•σ²_x
σ²_T = 100 × 40
σ²_T = 4000
To read the line plot in order to answer this question, you will need to understand that each X above the numbers represents the number of hours 1 student studied. If you count the total number of Xs, that would represent the total number of students surveyed.
The number of students that studied at least four hours, would be the number of Xs that are at 4 or above. This means there were 4 students that studied for hours or more.
