Choose the correct histogram for the binomial distribution P(x) = C, xp*q"=X, and compute the mean and standard 1 deviation if n= 6 and p= 3

Suppose that the distribution of the lifetime of a car battery produced by a certain car company is well approximated by a normal distribution with a mean of 1900 hours and variance 104. What is the approximate probability that a batch of 100 car batteries will contain at least 20 whose lifetimes are less than 1801 hours?

Suppose that a recent article stated that the mean time spent in jail by a first–time convicted burglar is 3.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 45 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.4 years. Suppose that it is somehow known that the population standard deviation is 1.1. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

Suppose that a distribution of 300 items has mean 115 and standard deviation 4. Find the z-score of the item x = 121