statistics

In a certain high court cases, the probability of acquittal by a five-man jury is 2/5. If X is the number of convictions in the next six trials,
i) Give the distribution of X
ii) Find the probability of at least three convictions
c) A random variable has a Poisson distribution with A=6 find
i) The probability that X is greater than 5
ii) P (2<x<7)

Two treatments were applied on maize
crop on two different plots and the yields were as follows.
Plot A 12 16 13 24 6 10 9 18
Plot B 17 13 16 4 8 10 17 5 8 23
Test at 5% whether the two treatments are statistically different

A random sample of 50 account balances from a firm extracted from a large number of debtors account gave a mean debt balance of 5932, with a standard deviation of 1150.
i) Construct a 96% confidence interval for the average debtors account balances for the firm.
ii) What sample size would be required if the population estimate is to be within 200 and at
96% confidence interval.

Four popular weight loss programs are considered, and the results were as recorded below
Low calorie 8 9 6 7 3 5 6 7 4
Low fat 2 4 3 5 1 3
Low carbohydrate 3 5 4 2 3 1 4
Control 2 -1 0 1 3
a) Obtain the ANOVA table for the above data
b) Test at α=5% if there is an overall difference in the mean weight loss among the four diets