For this binomial distribution, what is the variance for the number of successes when sample size is 76 with a probability of 0.46?

Last​ year, a person wrote 118 checks. Let the random variable x represent the number of checks he wrote in one​ day, and assume that it has a Poisson distribution. What is the mean number of checks written per​ day? What is the standard​ deviation? What is the​ variance?

The mean weight of an adult is 71 kilograms with a variance of 100.   If 181 adults are randomly selected, what is the probability that the sample mean would differ from the population mean by less than 1.2 kilograms? Round your answer to four decimal places.

Suppose the horses in a large stable have a mean weight of 873lbs, and variance of 17,161. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 50 horses are sampled at random from the stable? Round your answer to four decimal places.

Suppose a batch of metal shafts produced in a manufacturing company have a variance of 7.84 and a mean diameter of 201 inches. If 89 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be less than 201.2 inches? Round your answer to four decimal places. don't forget to round

Suppose a researcher pbserves a population of 12 people and computes SS=204. What is the variance? What is the standard deviation?