A coin will be tossed 7 times. Find the probability that there will be exactly 2 heads among the first 4 tosses, and exactly 2 heads among the last 3 tosses. (Include 2 digits after the decimal point.)

The population proportion is 0.25. What is the probability that a sample proportion will be within (plus or minus)+-0.05 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table.

a. n=100

b. n=200

c. n=500

d. n=1,000

e. What is the advantage of a larger sample size?

With a larger sample, there is a (lower/higher) probability will be within (plus or minus) +-0.05 of the population proportion .

The probability of receiving a A in Prob & Stats is 20%. Random picking students in a class. What is the probability that you have to select more than 3 students to get one student with A.

Group of answer choices

48.8%

20%

38.4%

87.2%

1. What is the probability of selecting each of the following at random from the population of IQ scores (mean=100, SD=15)

1. A person whose IQ is between 90 and 120?

2. A person whose IQ is below 75?

3. A person with an IQ above 80 AND a person with an IQ below 110? (Note: you are looking for two people here -- one with an IQ above 80 and the other with an IQ below 110.)

It is important to keep the probability of making Type I equal to α. With a t-test, how do we keep the probability of Type I error in check?

It is important to keep the probability of making Type I equal to α. With a t-test, how do we keep the probability of Type I error in check

Can you please assist with a conclusion for statics and probability samples

What is the Common Rule in probability and statistics and why does it exist in the United States?

just need second thought will give great comments and feedback (:

The ABC Co. is considering a new consumer product. They believe there is a probability of 0.30 that the XYZ Co. will come out with a competitive product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive product, their expected profit is $45,000; if they add an assembly line and XYZ does follow, they still expect a $12,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a profit of $450,000; if XYZ does compete for this market, ABC expects a loss of $80,000. If ABC does nothing, XYZ does nothing.

(a) Determine the EMV of each decision.

(b) Determine the EOL of each decision.

(c) Compare the results of (a) and (b).

(d) Calculate the EVPI.

1. On the basis of a physical examination, a doctor determines the probability of no tumour   (event labelled C for ‘clear’), a benign tumour (B) or a malignant tumour (M) as 0.7, 0.2 and 0.1 respectively.

A further, in depth, test is conducted on the patient which can yield either a negative (N) result or positive (P). The test gives a negative result with probability 0.9 if no tumour is present (i.e. P(N|C) = 0.9). The test gives a negative result with probability 0.8 if there is a benign tumour and 0.2 if there is a malignant tumour.

(i) Given this information calculate the joint and marginal probabilities and display in the table below.

2. What is the marginal probability the test result will be negative?
3. Obtain the posterior probability distribution for the patient when the test result is

            a) positive,   b) negative

4. Comment on how the test results change the doctor’s view of the presence of a tumour.

2. (i) A continuous variable X defined on the interval (1, ∞) has p.d.f given by f(x) = 1/x²

Derive the corresponding cumulative density function and graph it

(ii) Can the function f(x) = 1/x² define a p.d.f over the interval (2, ∞)? Explain your answer.

3. In the context of a discrete variable, X, show that the formula for variance of the variable can be written as Var(X) = E(X²) – [E(X)]²

4. Suppose that f(x) = 1/5 , x = 1, 2, 3, 4, 5 and zero elsewhere is the p.d.f. of the discrete random variable X. Compute E(X) and E(X²).

Use these results to find E[(X+2)²]

5. In question 4, calculate Var(X).