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statuscvo [17]
3 years ago
9

The graph below illustrates the time students took to complete a test when all students were allowed to finish. The distribution

has mean 65 minutes and standard deviation 10 minutes.Using the Empirical Rule, if the instructor sets a time limit of 75 minutes, at least _____% of students should be able to finish because this is one standard deviation above the mean.
Mathematics
1 answer:
Greeley [361]3 years ago
7 0
The answer for this question is 15%
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John and Jane are married. The probability that John watches a certain television show is .7. The probability that Jane watches
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a) The probability  that both John and Jane watch the show is 0.12.

b.The probability that Jane watches the show, given that John does is  0.1714.

c)They do watch show independent of each other.

Step-by-step explanation:

Here, as given in the question:

Probability that John watches a certain show  = 0.7   ⇒ P(J) = 0.7

Probability that Jane watches a certain show  = 0.3   ⇒ P(Je) = 0.3

Probability that John watches a certain show given Jane watches it to

 = 0.4   ⇒ P(J/Je) = 0.4

a. )  Here, we need to find the probability of  both Jane and John watching a show , P(J∩Je)

Now, by BAYES THEOREM:

P(J/Je)  = \frac{P(J \cap Je)}{P(Je)}

\implies  0.4  = \frac{P(J \cap Je)}{0.3} \\\implies P(J \cap Je) = 0.4 \times 0.3  = 0.12

Hence the probability  that both John and Jane watch the show is 0.12.

b.) The probability that Jane watches the show, given that John does is P(J/Je)

By BAYES Theorem:

P(Je/J)  = \frac{P(J \cap Je)}{P(J)}\\\implies P(Je/J)  = \frac{0.12}{0.7}  = 0.1714

Hence, the probability that Jane watches the show, given that John does is  0.1714.

c) As we can see P(Jane ∩ John) =  0.12

So, the probability of both of them seeing the show TOGETHER is 0.12.

Hence, they do watch show independent of each other and the probability of doing that is 1.0.12  = 0.88

7 0
3 years ago
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