practicing and need help with detailed explanation. thanks.

1). A local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. They randomly selected 380 residents in the community and contacted them by telephone. Of the 380 residents surveyed, 306 supported the property tax levy. Let p represent the proportion of residents in the community that support the property tax levy. What is the 95% confidence interval for p?

2) You measure the lifetime of a random sample of 50 tires of a certain brand. The sample mean is 59. Suppose that the lifetimes for tires of this brand follow a Normal distribution, with unknown mean and standard deviation = 7 kg. A 95% confidence interval of is

3) Based on long experience, an airline has found that about 91% of the people making reservations on a flight from Miami to Denver do show up for the flight. Suppose there are 258 ticket reservations. What is the probability that more than 237 people will show up? Use the Normal approximation to the Binomial.

4) The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed with mean and standard deviation = 3.1. I select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields xx = 63. What is the margin of error for a 80% confidence interval for in days?

5). A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean = 38 minutes and standard deviation = 5 minutes. The drug is administered to one patient selected at random. What is the probability that the time it takes to go into effect is 35 minutes or less?