Question

Say we have a random sample of n = 15 people who visit a library’s website to browse their catalogue. With p = 0.1 of the population proportion who reserve a book while browsing, what is the probability of selecting exactly 14 users who actually make a reservation in the random sample

Answer 1

Answer with explanation:

For , n=15 people in  a random sample who visit a library’s website to browse their catalogue.

Also, probability = 0.1

        of the population proportion who reserve a book while browsing.

We have to calculate

⇒⇒ Probability of selecting exactly 14 users who actually make a reservation in the random sample, can be calculated in following way

¬¬If, n=15

Probability = 0.1

We will find actual number of users out of 15 who reserves a book while browsing if probability of reserving a book while browsing is 0.1.

$\frac{x}{15}=0.1\\\\x=1.5$

It means out of 3 population only 2 of them reserve a book while browsing.

So, if there are 14 users who actually make a reservation in the random sample, then total random sample will be

  =14 × 1.5

 =21 in all

So, Required probability

          $=\frac{\text{Total sample who reserves a book while browsing}}{\text{Total Random Sample}}\\\\=\frac{14}{21}\\\\=\frac{2}{3}$