Time spent using email per session is normally distributed with a mean of 20 minutes and...

Time spent using email per session is normally distributed with a mean of 20 minutes and a standard deviation of 3 minutes.

(a) What is the probability that time spent using email per session is greater than 21 minutes?

(b) What is the probability that time spent using email per session is between 18.3 minutes and 22.6 minutes?

(d) Explain the difference between the results in part (a) and part (c).

Solutions

Expert Solution

Let X is a random variable shows the time spent using email per session. Here X has normal distribution with parameters as follows:

(a)

The z-score for X = 21 is

The probability that time spent using email per session is greater than 21 minutes is

(b)

The z-score for X = 18.3 is

The z-score for X = 22.6 is

The probability that time spent using email per session is between 18.3 minutes and 22.6 minutes is

(c)

The z-score for is

The probability that a random sample of 64 email users will spend an average time greater than 21 minutes is

(d)

The result of part (c) give probability that average time greater than 21 minutes (for sample size 24) while result of part (a) give probability that individual time is greater than 21 minutes.

orchestra answered 1 year ago

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