Question

A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are shown. 10 gumballs are red 8 gumballs are blue 5 gumballs are green 2 gumballs are white.Based on the random sample results, complete the prediction statements for the entire machine of 200 gumballs.

There are
? red gumballs in the machine.
There are
? more green gumballs than white gumballs in the machine.
There are
? gumballs that are either blue or green in the machine.

Answer 1

• 80 red
• 24 more green than white
• 104 are blue or green

Explanation:

Given a sample of 25 gumballs that had 10 red, 8 blue, 5 green, and 2 white gumballs, you want estimates for 200 gumballs of ...

• the number of red
• how many more green than white
• the number of blue or green.

Estimate

The sample size is 1/8 of the total number of gumballs in the machine, so our estimates will be 8 times the corresponding sample values.

Red

We estimate 8 · 10 red = 80 red gumballs in the machine.

Green -White

The sample has 5 green and 2 white, so 5-2 = 3 more green than white.

We estimate 8 · 3 = 24 more green than white in the machine.

Blue or Green

There are 8 + 5 = 13 blue or green gumballs in the sample.

We estimate 8 · 13 = 104 blue or green gumballs in the machine.

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