Search & Filtering
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
4. What is the difference between continuous data and discrete data? Give a real-world example of each.
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?
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)
(a) If X has a Uniform Distribution in (−𝑎, 𝑎), 𝑎 > 0 , find 𝑎 such that 𝑃(|𝑋| < 1) = 𝑃(|𝑋| > 1). Also find 𝑃(|𝑋 − 1| < 2) and 𝑃(|𝑋| > 2).
(b)If X has a uniform distribution in (0, 3) ant Y has exponential distribution with parameter α, find α that 𝑉𝑎𝑟(𝑋) = 𝑉𝑎𝑟(𝑌). Also find 𝑃(𝑌 > 0.5/𝑌 < 1) .
