A movie critic rates movies on a scale of 4 stars (excellent) to 1 star (worthless). A summary of her ratings for 20 movies is shown in the table.

Question

The table titled movie ratings show 3 movies with 4 stars, 7 movies with 3 stars, 6 movies with 2 stars, 4 movies with 1 star.

If the critic rates a total of 100 movies, what is the best prediction for the number of movies she gives exactly 3 stars?

A.
35

B.
27

C.
47

D.
50

Answer 1

To predict the number of movies the critic gives exactly 3 stars, we can use the proportions from the data provided for the 20 movies.

From the table:

• 3 movies received 4 stars
• 7 movies received 3 stars
• 6 movies received 2 stars
• 4 movies received 1 star

First, we find the total number of stars rated:

• Total movies rated: \(3 + 7 + 6 + 4 = 20\)

Now let's find the proportion of movies that received 3 stars:

• Proportion of 3-star movies: \(\frac{7}{20}\)

Now we can project this proportion to the total of 100 movies. To find the expected number of movies with 3 stars: \[ \text{Number of 3-star movies} = \left( \frac{7}{20} \right) \times 100 \] \[ = 35 \]

Thus, the best prediction for the number of movies she gives exactly 3 stars is:

A. 35