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Dmitry [639]
3 years ago
11

The length of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of .7 mi

nutes. What is the probability that a conversation lasts longer than 6 minutes?
Mathematics
2 answers:
Charra [1.4K]3 years ago
7 0

The <em><u>correct answer</u></em> is:

0.0764

Explanation:

We will use a z-score to answer this.  The formula for a z-score is

z=\frac{X-\mu}{\sigma}, where μ is the mean and σ is the standard deviation.  Using our information in this problem, we have

z=\frac{6-5}{0.7}=\frac{1}{0.7}=1.43

Using a z-table, we look up the z-score 1.43.  The area under the curve to the left of, or less than, this value is 0.9236.  This means the probability that the time is greater than this is 1-0.9236 = 0.0764.

AVprozaik [17]3 years ago
3 0
The z-score for 6 minutes is:
z=\frac{X-\mu}{\sigma}=\frac{6-5}{0.7}=1.429
Reference to a standard normal distribution table gives the result:
P(length > 6) = 0.077
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Answer:

P(A or B) = P(A) + P(B) - P(A and B) = 0.5 + 0.7 - 0.3 = 0.9

Step-by-step explanation:

The equation we should use to calculate the addition of probabilities is:

P(A or B) = P(A) + P(B) - P(A and B)

Notice that if we just sum P(A) + P(B), our result would be wrong, because we would sum the intersection of those events two times.

So, in this case, if we call 'A' the pillow being encased in microfiber and 'B' the pillow being filled with memory foam, we have that:

P(A) = 0.5

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P(A and B) = 0.3

So the addition of both probabilities is:

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3 years ago
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Step-by-step explanation:

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seropon [69]
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Hope this helps!

:)

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