Answer:
<u>Part 1:</u> 1.5492
<u>Part 2:</u> 0.0035
<u>Part 3:</u> 0.0173
<u>Part 4:</u> 0.8358
Step-by-step explanation:
Number of cases, n = 15
Probability they can be resolved same day = 0.8 [p=0.8]
<u>Part 1:</u>
<u>What is the Standard Deviation?</u>
The formula is
Plugging in we get:
Standard Deviation is 1.5492
<u>Part 2:</u>
<u>What is the probability 7 of the problems can be resolved today?</u>
Since this is binomial probability, the formula is:
Here, r = 7, so we plug in what we know and get out answer:
THe probability is 0.0035
<u>Part 3:</u>
"OR" in probability means "+", so we add
P(x=7) + P(x=8)
We already know P(x=7), we just find P(x=8) now.
Replacing r = 7 with r = 8 into the formula above, we get:
The probability is 0.0138
Hence P(x=7) + P(x=8) = 0.0035 + 0.0138 = 0.0173
<u>Part 4:</u>
More than 10 problems means P(x=11) + P(x=12) +....P(x=15)
we have to plug in 11,12,13,14,15 into r of the formula individually and find each and sum them.
The same process.
Basically it is going to be:
<em>P(x>10) = P(x=11) + P(x=12) + P(x=13) + P(x=14) + P(x=15)</em>
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The answer after substituting and summing would be 0.8358 [using binomial calculator and table for ease]