Statistics and Probability Answers

When an unbiased coin is tossed seven times, what is the probability of obtaining at least 3 tails?

When an unbiased coin is tossed seven times, what is the probability of obtaining at least 4 heads?

Assuming the following table of the cost (X) and selling (Y) price of flight tickets in dollars ($):

Cost Price

(X)

Sell Price

(Y)

200 300

230 250

500 510

540 700

670 730

320 500

190 412

280 355

625 635

Compute the following:

1. Plot a scatter plot of the data (manual plot or use any software like excel). (2 marks)

2. Pearson correlation coefficient (r). (2 marks)

3. The relation type and strength. (1mark)

4. Linear regression formula (𝑌̂

𝑖 = 𝛽̂

0 + 𝛽̂

1𝑋𝑖

). (2 marks)

5. The estimated of the ticket selling price when the cost is $500. (1 mark)

6. The error of the ticket selling price estimate when the cost is $500. (1 mark)

7. What is the percent of cost price variable interpret the variation of sell price variable

(How much the coefficient of determination)? (1 m

Let X∼Poisson(k−1)X∼Poisson(k−1) with Var(X)=1Var(X)=1, then find the value of the constant kk

Two cards are drawn from a well shuffled pack of playing cards. Calculate the probability of the

events (i) there is one card of black suits and other of red suits, (ii) both the card are aces (iii)

both the cards are hearts

Out of 25 employees of a company, 5 are engineers. Three employees are selected at random for granting leave. What is the probability that (i) all the three are engineers?(ii) none of them is an  engineer? (iii) at least one of them is an engineer

1.If 100 people are selected at random, what is the chance that not more than ten people suffer from COVID 19-disease

2. Does talking on mobile phones while driving distract people? Researchers measured the reaction times of 80 study

participants as they talked on mobile phones and found that the average level of distraction from their driving was

rated to be 60 percent. Explain what could be your population, Sample, sample statistic and characteristic.

Suppose that the annual income of a fast-food chain is normally distributed with a mean of $72,000 and a standard deviation of $9,000. a. What is the probability that a randomly selected fast-food restaurant will generate an annual income between $65,000 and $75,000? (2 Marks) b. What is the probability that a randomly selected fast-food restaurant will generate an annual profit of more than $80,000? (2 Marks) c. What minimum income does a fast-fast restaurant need to earn to be in the top 5% of incomes? (2 Marks) 3 d. What maximum income does a fast-food restaurant need to earn to be in the bottom 30% of incomes? (2 Marks)

Suppose that the distribution of weights of Philippine hamsters is normally distributed with a mean of 65.5 g and standard deviation of 11.6 g. If there are 1000 weights in this population, how many of them are greater than or equal to 79 g?

A deck of cards contains 24 cards where 4 are red. If 6 cards are drawn at random without replacement from this deck, what is the probability that no red cards are drawn?