Kindly help me find the solutions o all of the following questions please?

Find the probability of passing if the lowest

grade is 15 correct out of 20.

4 A new surgical procedure is said to be successful 80% of times.

Suppose the operation is performed five times, and the results

are assumed to be independent of one another. What are the

probabilities of these events

a All five operators are successful.

b Exactly four are successful.

c Less than two are successful.

d More than 3 are successful

e Find the variance and the standard deviation

5 A study found that 1% of social security recipients are too

young to vote, if 800 social security recipients are randomly

selected. Find the mean, variance, and the standard deviation

of the number of recipients who are too young to vote.

6 If 3% of calculators are defective, find the mean, variance, and

standard deviation of a lot of 300 calculators.

7 Thirty-two percent of adult Internet users have purchased

products or services online. For a random sample of 200 adult

Internet users, find the mean, variance, and standard deviation

for the number who have purchased good, or services online

4. (10+ 10 = 20 points) The Q-function is defined as the fail probability of a standard Gaussian random variable. Specifically, Q(a) = P(Z 2 0) is the probability that the standard Gaussian random variable Z is larger than the value a. (b) Suppose that X is a Gaussian random variable with mean a and variance o', Express the probability P(X 2 2) in terms of Q(s).X and Y are jointly Gaussian random variables. Which one of the following statements is not necessarily true? 0 X + Y and X + 2Y are also two jointly Gaussian random variables. 0 X + Y and X - Y are also two jointly Gaussian random variables. 0 5+2X+Y has a Gaussian distribution 0 X + Y and X Y are independent. 0 X and Y are uncorrelated if and only ifthey are independent. 0 X + Y is a Gaussian random variable. Generating a pair of independent Gaussian random variables: Understand the procedure in 5.10 Generating independent Gaussian random variables of the textbook. Write a Matlab code that generates a pair of independent Gaussian random variables and displays the following. You can use other programming tools available. (a) Histograms for a Gaussian random variable for 1000 and 5000 samples. (b) Scattergrams for 1000 and 5000 pairs of Gaussian random variables. What to submit: one pdf file that contains the following. Only pdf file type is allowed for upload. (25pt) Description of the method with your code (25pt) Two histogram figures for 1000 and 5000 samples. Refer to Figure 5.28 (25pt) Two scattergrams for 1000 and 5000 pairs of Gaussian random variables. Refer to Figure 5.29 (25pt) Your comments on the resultsGenerating a pair of independent Gaussian random variables Understand the procedure on page 296 of the textbook. Write a Matlab code that generates a pair of independent Gaussian random variables and displays the following. You can use other programming tools. (a) Histograms for a Gaussian random variable for 1000 and 5000 samples. (b) Scattergrams for 1000 and 5000 pairs of Gaussian random variables. What to submit: one pdf file that contains the following. Description of the method with your code Two histogram figures for 1000 and 5000 samples. Refer to Figure 5.28 Two scattergrams for 1000 and 5000 pairs of Gaussian random variables. Refer to Figure 5.29 Your comments on the results