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Given in the question that, The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of$\$4.59$and a standard deviation of $\$0.10$. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the $16$gas stations.

According to the information given in the question,

The mean of the unknown distribution$=\$4.59$

The standard deviation$=\$0.10$.

The sample size$=30$.

Let's use the $Ti-83$calculator to find the probability that the average price for 30 gas stations is less than $\$4.55$

For this, click on localid="1648491577015" $2^{\text{nd}}$,

then DISTR, and then you can enter the provided details by scrolling down to the 'normalcdf' option.

Then, to get the desired result, press the calculator's ENTER button.

The following screenshot will assist us in comprehending the approach.

Hence, the probability that average price for $16$gas stations is over $\$4.69$is $.01419$. Thus, the probability is almost near to $0.0142$.

Therefore, option 'c' is the correct answer