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The average amount of money spent for lunch per person in the college cafeteria is $\$7.15$ and the standard deviation is $\$2.48$. Suppose that $48$ randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to $4$ decimal places where possible. What is the distribution of $X$? $X \sim N(,$) What is the distribution of $\bar{x}$? $\bar{x} \sim N(,$) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $\$6.77$ and $\$7.27$. For the group of $48$ patrons, find the probability that the average lunch cost is between $\$6.77$ and $\$7.27$. HINTS: $\$2.48$$0$ $\$2.48$$1$ To find $\$2.48$$2$ use normalcdf$\$2.48$$3$ $\$2.48$$4$ $\$2.48$$5$ When you are looking for the probability of one value the $\$2.48$$6$ Submit