In 2016, the mean price per gallon of regular gasoline sold in the USA was $2.76. Assume the populations mean price per gallon is $2.76, and the population standard deviation is $0.83. Suppose that a simple random sample of 47 gas stations will be selected and a sample mean price per gallon will be computed using data collected from the 47 gas stations.

What is the probability that the simple random sample will provide a sample mean in between $2.70 and $2.87? Round all answers to three decimal places.