According to a Survey, households in the city X spend an average of $24 per week on their leisure activities. Suppose you are given a sample of 100 households and that the population variance is 36....

please answer the last three questions c),d),e)

Extracted text: According to a Survey, households in the city X spend an average of $24 per week on their leisure activities. Suppose you are given a sample of 100 households and that the population variance is 36. a) What is the population standard deviation? What is the standard deviation of the sample average? b) What is the probability that the sample average spend more than $25? c) What is the probability that the sample average spend exactly $23? d) What is the probability that the sample average spend between 23.5$ and 24.5$? e) Suppose that the population standard deviation is unknown. If 8% of all sample means are smaller than 20 and the population mean is still 24, what is the value of the standard deviation? f) Suppose that the population mean is unknown. If 15% of all sample means are smaller than 24 and the population standard deviation is still as in question a), what is the value of the population mean?