alisha bought a collection of 500 old pennies. she chose 20 pennies from the collection and recorded their…

alisha bought a collection of 500 old pennies. she chose 20 pennies from the collection and recorded their dates. seven pennies had dates earlier than 1980. what is the best estimate of the percent of pennies in alishas collection that have dates earlier than 1980? enter your answer in the box. %

alisha bought a collection of 500 old pennies. she chose 20 pennies from the collection and recorded their dates. seven pennies had dates earlier than 1980. what is the best estimate of the percent of pennies in alishas collection that have dates earlier than 1980? enter your answer in the box. %

Answer

Explanation:

Step1: Set up the proportion

We use the sample - to - population ratio. In the sample of 20 pennies, 7 have dates earlier than 1980. Let $x$ be the number of pennies with dates earlier than 1980 in the population of 500 pennies. The proportion is $\frac{7}{20}=\frac{x}{500}$.

Step2: Solve the proportion for $x$

Cross - multiply: $20x = 7\times500$. Then $20x=3500$. Divide both sides by 20: $x=\frac{3500}{20}=175$.

Step3: Calculate the percentage

The percentage of pennies with dates earlier than 1980 in the collection is $\frac{175}{500}\times100%$. $\frac{175}{500}\times100%=\frac{17500}{500}=35%$.

Answer:

35%