A band sold out a concert with 4200 seats. A random sample of 120 ticket buyers is surveyed and 28 buyers made their purchase on the first day the tickets went on sale. How many of the 4200 tickets are likely to have been sold on the first day they were available? Show your work.

28/120 = 0.23333 = 23%

0.23 * 4200 = ?

so the answer is 966?

Yes, 966.

Thank you!

You're welcome.

To estimate the number of tickets sold on the first day, you can use the concept of proportions.

First, calculate the proportion of ticket buyers who made their purchase on the first day out of the entire sample:
Proportion = (Number of buyers on the first day) / (Sample size)
Proportion = 28 / 120
Proportion ≈ 0.2333

Next, use this proportion to estimate the number of ticket buyers who made their purchase on the first day out of the whole population of 4200 ticket buyers:
Number of buyers on the first day = Proportion * Total number of ticket buyers
Number of buyers on the first day = 0.2333 * 4200
Number of buyers on the first day ≈ 978.36

Since you cannot sell a fraction of a ticket, round the estimated number to the nearest whole number:
Estimated number of tickets sold on the first day ≈ 978

Therefore, it is estimated that approximately 978 tickets were sold on the first day they were available.