Question

The average time it takes a certain brand of ibuprofen to start working is 25 minutes, with a standard deviation of 13 minutes, distributed normally. A pharmacist randomly samples 20 pills from this brand, because she is researching different brands in order to find the quickest acting ibuprofen to recommend to her customers. Identify the following to help her make her recommendations, rounding to the nearest hundredth if necessary:

a. mu = ______ minute
b. sigma = ______ minute
c. n = ______
d. mu-x = _______ minute

Answer 1

(a)
`\mu=25\ \text{minutes}`

(b)
`\sigma=13\ \text{minutes}`

(c)
`n=20`.

(d)
`\mu_(\bar x)=\mu=25\ \text{minutes}`

Explanation:

Let the random variable X represent the time it takes a certain brand of ibuprofen to start working.

(a)

The mean time it takes a certain brand of ibuprofen to start working is, 25 minutes.

That is,
`\mu=25\ \text{minutes}`.

(b)

The standard deviation of time it takes a certain brand of ibuprofen to start working is, 13 minutes.

That is,
`\sigma=13\ \text{minutes}`.

(c)

The sample selected by a pharmacist is of size, 20.

That is,
`n=20`.

(d)

The mean of the sample means is:

`\mu_(\bar x)=\mu=25\ \text{minutes}`