Statistics and Probability Answers

How much does ten pounds of weight change the estimated number of cups of dog

food consumed? Dog 1 2 3 4 5 6 7 8 9

Weight 0.41 1.48 0.79 0.41 0.85 1.11 0.37 1.11 0.41

Consumption in cups 3 8 5 4 5 6 3 6 3

Dog 10 11 12 13 14 15 16 17 18

Weight 0.91 1.09 2.07 0.49 1.13 0.84 0.95 0.57 1.68

Consumption in cups 5 6 10 3 6 5 5 4 9

Dog 1 2 3 4 5 6 7 8 9

Weight 0.41 1.48 0.79 0.41 0.85 1.11 0.37 1.11 0.41

Consumption in cups 3 8 5 4 5 6 3 6 3

Dog 10 11 12 13 14 15 16 17 18

Weight 0.91 1.09 2.07 0.49 1.13 0.84 0.95 0.57 1.68

Consumption in cups 5 6 10 3 6 5 5 4 9

Let η and ξ be two independent normal random variables with mean 1 and variance 2. Which of the

following statements is correct?

◦ η + ξ and η − ξ are uncorrelated and independent

◦ η + ξ and η − ξ are uncorrelated, but not independent

◦ η + ξ and η − ξ are correlated, but independent

◦ η + ξ and η − ξ are correlated and not independent

◦ None of the statements is correct

Question 2

In a study of hypertension and optimal treatment conducted by the National Heart Institute, 10,000 patients had a mean systolic blood pressure (BP), 𝝁 = 𝟏𝟔𝟏 mm Hg and standard deviation, 𝝈 = 𝟐𝟓 mm Hg. Assume the systolic blood pressure is normally distributed.

a. What is the probability of patients with a systolic blood pressure of more than 180 mm Hg?

b. How many patients will have a systolic blood pressure of more than 180 mm Hg?

c. What is the probability of patients with a systolic blood pressure between 145 and 160 mm Hg?

d. If 60 random samples each of size 30 are drawn from this population, determine:

  i. the sampling distribution of the mean systolic blood pressure.

  ii. the probability that the of mean systolic blood pressure between 140 and 165 mm Hg.

Question 1

An airline company wishes to know the proportion of business class travelers flying the Kuala Lumpur-to-Hong Kong route. In a random sample of 350 passengers, 190 are business class passengers.

a. Determine the point estimate of the true proportion of business class passengers.

b. Construct a 95% confidence interval estimate of the average waiting time for all customers.

c. Construct a 99% confidence interval estimate of the average waiting time for all customers.

d. Referring to b) and c), what will happen to the width of confidence interval?

A random sample is size n = 2 are drawn from a finite population consisting of the numbers 3,4,5,6 and 7

A company responds to 80% of all enquiries within 2 working days. The firm received 8 enquiries today. What is the probability that all the 8 enquiries are responded within 2 working days?

a.

0.0839

b.

0.3356

c.

0.1678

d.

0.6422

In a group of 125 computer users, 50 of them have a GPU installed in their systems, 30 of them have SSD storage, and 15 have both. If a computer user chosen at random has a GPU, what is the probability he/she also has an SSD?

In a group of 125 computer users, 50 of them have a GPU installed in their systems, 30 of them have SSD storage, and 15 have both. If a computer user chosen at random has a GPU, what is the probability he/she also has an SSD?

adnan is the branch manager at a local insurance company. recently, adnan’s been receiving customer feedback saying that the wait times for a client to be served by a customer service representative are too long. adnan decides to observe and write down the time spent by each customer on waiting. here are his findings from observing and writing down the wait times spent by 42 customers:

Let 𝑋~𝑁(40,144) and if 𝑌 = 2𝑋 − 1

Find the following probabilities:

(i) 𝑃(𝑋 ≤ 40)

(ii) 𝑃(𝑌 ≥ 50)

(iii)𝑃(35 ≤ 𝑋 ≤ 45)

(iv)𝑃(−45 ≤ 𝑌 ≤ 45)

(v)𝑃(−50 ≤ 𝑌 ≤ 100)