Statistics and Probability Answers

2. Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as shown
below;
X 1 2 3 4 5 6
P(X=x) 1/6 1/6 1/5 k 1/5 1/6
a) Find;
(i) the value of k.
(ii) E(X)
(iii) E(X2
)
(iv) Var(X)
(v) P(1 X <5)

The distribution of duration of unemployment for all 18-24 year-old Americans is nearly normal with mean 12.7 weeks and standard deviation 0.3 weeks. Suppose we randomly sample 20 people from this population, ask them about the duration of their unemployment (in number of weeks), and record the sample mean. We repeat this 5,000 times, and build a a distribution of sample means. What is the name of this distribution?

A. randomization distribution
B. sampling distribution
C. sample distribution
D. population distribution
E. bootstrap distribution

2. Which of the following is false regarding paired data?

A. Each observation in one data set has a natural correspondence with exactly one observation from the other data set.

B. Each observation in one data set is subtracted from the average of the other data set's observations.

C. In a paired analysis we first subtract the paired observations from each other, and then do inference on the differences.

D. Two data sets of different sizes cannot be analyzed as paired data.

1.Which of the following is false about bootstrapping?

A. The endpoints of a 95% bootstrap confidence interval are the cutoff values for the top and bottom 2.5% of the bootstrap distribution.

B. Bootstrap distributions that are extremely skewed or have isolated clumps of values may yield unreliable confidence intervals.

C. Bootstrap distributions are constructed by sampling with replacement from the original sample, while sampling distributions are constructed by sampling with replacement from the population.

D. A bootstrap confidence interval constructed based on a biased sample will still yield an unbiased estimate for the population parameter of interest.

Eric’s average income for the first 4 months of the year is $1,450.25, what must be his
average income for the remaining 8 months so that his average income for the year is
$1,780.75?

Blood pressure is an important health indicator in humans. Blood pressure results from two forces. One, the systolic pressure, is created by the heart as it pumps blood into the arteries and through the circulatory system. The other, the diastolic pressure, is the force of the arteries as they resist the blood flow. In a particular population the systolic pressures are normally distributed with a mean of 110 mmHg and a standard deviation of 8 mmHg.

(a) Systolic pressure less than 120 mmHg are considered normal. What percentage of the population has normal systolic blood pressures?

(b) Systolic pressures above 140 mmHg are considered hypertensive and in need of medical intervention. What proportion of the population will have these values?

(c) Systolic pressures of 120 to 139 mmHg are considered

The life time of a certain brand of bulbs produced by a company is normally
distributed, with mean 210 hours and standard deviation 56 hours. What is the
probability that a bulb picked at random from this

a. According to the Ministry of Health, the height of Guinean travellers who were quarantined in Tamale for the novel coronavirus were normally distributed about a mean of 160cm and a standard deviation of 8cm. Find the probability that a traveller selected at random has. Height between 148cm and 175cm, Height above 164cm, Height below 179cm. b.The average time taken for the nearest Covid-19 ambulance team to convey a patient showing symptoms to the nearest designated hospital follows the normal distribution about a mean of 60 seconds and a standard deviation of 8 seconds. If 200 patients were selected at random, how many of them could be taken to the hospital in. Less than 50 seconds, More than 64 seconds, The Shelf life of a particular dairy product is normally distributed with a mean of 12 days and a variance of 9 days. About what percentage of the products last between 13 and 16 days

The life time of a certain brand of bulbs produced by a company is normally distributed, with mean 210 hours and standard deviation 56 hours. What is the probability that a bulb picked at random from this company's products will have a lifetime of ; 1. At least 300 hours
2. At least 100 hours
3. Between 150 and 250 hours

Emmanuel is given a multiple-choice exam with ten questions and each question with
five possible answers. He decided to guess randomly for each question. What is the
probability that he will get at least six questions correct?