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3. (14 pts) A population of 1,500 students spends an average of $12.50 a day on dinner. The standard deviation of the expenditure is $4. A simple random sample of 81 students is taken. a. What is the expected value, standard deviation, and shape of the sampling distribution of the sample mean? Explain the reason. Which theorem ensures the shape of the sampling distribution? b. What is the probability that these 81 students will spend a combined total of more than $1077.3? c. What is the probability that these 81 students will spend a combined total between $1060.09 and $1098.53