LEARNING OBJECTIVE: Identify the percent of data that is between two values using a given standard deviation, mean, and the 68-95-99.7 rule.

At a nearby frozen yogurt shop, the mean cost of a pint of frozen yogurt is $\mathrm{\$}1.50$ with a standard deviation of $50:10$.
Assuming the data is normally distributed, approximately what percent of customers are willing to pay between $\mathrm{\$}1.30$ and $\mathrm{\$}1.70$ for a pint of frozen yogurt?
a) $99.7\mathrm{\%}$
b. $34\mathrm{\%}$
c.) $68\mathrm{\%}$
d.) $95\mathrm{\%}$

Step 1 ：Calculate how many standard deviations away from the mean our two values are. For $1.30, subtract the mean from this value and divide by the standard deviation: $(1.30-1.50)/0.50=-0.4$ standard deviations away from the mean.

Step 2 ：Do the same for $1.70: $(1.70-1.50)/0.50=0.4$ standard deviations away from the mean.

Step 3 ：We are looking for the percentage of data that falls within -0.4 and 0.4 standard deviations of the mean.

Step 4 ：According to the 68-95-99.7 rule (also known as the empirical rule), approximately 68% of data in a normal distribution falls within one standard deviation of the mean.

Step 5 ：Since -0.4 and 0.4 standard deviations are less than one standard deviation away from the mean, we can conclude that the percentage of customers willing to pay between $1.30and$1.70 for a pint of frozen yogurt is less than 68%.

Step 6 ：Therefore, the correct answer is: $\boxed{{\displaystyle 34\mathrm{\%}}}$