Need help for couple of statistics problems

A study showed that none of the patients treated with Malaria recovered in 50% of the cases. During a period in which 600 patients were treated, what is the probability that no patient recovered in 350 or more of the treated cases, and 140 or less of the treated cases?

How large a sample would be needed to form a 60% confidence interval for the mean nicotine content of a brand of cigarettes if the nicotine content has a normal distribution with sigma equal to 8.5 mg and the width of the interval (the length of the confidence interval) equal to 6 mg to satisfy testing requirements?

Suppose that the average weekly expense of college students is $60 with a variance of 100. Suppose, furthermore, that we take a random sample of 2,500 college students and calculate their average arithmetic weekly expenditure. What is the probability that it will fall between $59.6 and $60.4?

What will the appropriate area under the curve be so as to calculate the value of μ?
a. 90 percent
b. 95 percent
c. 98 percent
d. 99 percent

A population consists of 9,988 persons. It has a mean height of 68 inches with a standard deviation of 3.44. Find the probability of getting a random sample of size five for which the arithmetic mean lies between 68.5 and 69.5.

Thank you very much


Omega Contributor
Which parts are you having difficulties understanding? Do not reply with all parts, be very specific about what you do not understand and what you have tried.
I am new to statistics and the book that the school assigned is crap, I feel like I can do it but the problem is I cannot identify which probability distribution these question are from?