assume the n trails is independent and that p is the probability of success on a given trail. Use the binomial probability formula to find P(x) n=5, x=3, p=0.3

We are picking 200 jelly beans out of a huge vat at a factory known to have 25% black jelly beans. Use the normal approximation to the binomial to find the probability that we get 60 or fewer black jelly beans

We break a stick at a uniformly chosen random location. Find the probability that the shorter piece is less than 1/5 of the original.

A group of people were asked if some psychics can help solve murder cases. 197 responded "yes", and 233 responded "no".  Find the probability that if a person is chosen at random, the person does NOT believes some psychics can help solve murder cases. Probability = (Round to 4 decimal places)

The Food Marketing Institute shows that 16% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.16 and a sample of 800 households will be selected from the population. Use z-table. Calculate (p), the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals). What is the probability that the sample proportion will be within +/- 0.02 of the population proportion (to 4 decimals)? What is the probability that the sample proportion will be within +/- 0.02 of the population proportion for a sample of 1,800 households (to 4 decimals)?

Assume it was determined from a random sample of customers that the probability of buying cake is 40%; the probability of buying ice cream is 62%; and the probability of buying cake or ice cream is 86%. What is the probability of buying chocolate ice cream and frozen yogurt? (Round your answer to 2 decimals)

Compute the probability of X successes using the binomial formula. Round your answers to three decimal places as needed. n=4,  p=0.68,  X=3 P(X)=

A local county has an unemployment rate of 6.1%. A random sample of 20 employable people are picked at random from the county and are asked if they are employed. The distribution is a binomial. Round answers to 4 decimal places. Find the probability that there are at most 2 in the sample are unemployed.

Assume that n 16, and p = 9/10. Find the probability of at least 2 successes and at least 3 failures.

Suppose we played roulette x5 times (where x = 3 is the last digit of your student ID) and each time we bet on the number 17. In each game, xthe probability of winning is 1/37. Calculate the probability P(X = z), where z is the second-to-last digit of your student ID (in this case, z = 5). Draw the probability distribution function graph for the given scenario. Also, calculate the probability of winning less than 5 timesDo this task in R commander.