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# Statistics

Duedate

Question1

1. Probability of drawing a queen: P(Queen) or 0.08

2. Probability of drawing a heart: P(Heart) or 0.25

3. Probability of drawing a red card: P(Red card) or 0.50

Question2

1. Probability of selecting a person with blood group : P( or 0.06

2. Probability of choosing a person with blood type

P(

1. Probability of not selecting a person with blood type:

Thus

Question3

 Incident Swerved Sped up Cut off a car Almost hit a car Number of incidents 44 40 20 19

Thetotal number of incidents is 123

Theprobability that a randomly chosen event involves cutting off a caris

Question4

1. Simple event

2. Not a simple event

3. Simple event

Question5

Thefundamental counting principle is a standard way of determining thenumber of ways two or more operations can be performed. Using thisprinciple the number of different shirts available from the companyis

Question6

Classicalprobability is a statistical measure of equally likely cases.

Asubjective probability is a statistical measure derived from thepersonal judgment of the researcher about whether a particularoutcome will occur

Empiricalprobability is a measure of the likelihood that tackles real lifesituations rather than theoretical cases.

1. Classical probability

2. Subjective probability

3. Empirical probability

Question7

Twoevents are said to be dependent on each other if the results of thesecond experiment are affected by the results of the previous test.

1. Independent events

2. Dependent events

Question8

Letthe event that the student is a sophomore be A and the event that thestudent does not own a credit card be B. These events are dependenton each other. Therefore

Thus

Question9

Thereare 52 cards among which 4 are &quoteights.&quot Therefore, let thefirst &quoteight&quot card chosen be A and the second card be B.

.Thus

Question10

Twoevents are said to be mutually exclusive if the occurrence of oneevent precludes the occurrence of the other.

1. Not mutually exclusive

2. Mutually exclusive

Question11

Thestated events can occur at the same time hence they are not mutuallyexclusive events.

Question12: Part I

Acombinatorial arrangement is one in which the order in which theelements are put does not matter. On the other hand withpermutations, the arrangement of items is of paramount importance. Wecould say a permutation is an ordered combination

1. Permutation

2. Permutation

3. Combination

Question12: Part II

nCrgives the possible combinations of the five numbers

where60C5 .There are 5,461,512 possible combinations of the five numbers. Bybuying one ticket, the probability of winning the lottery is

Question13

Adiscrete variable takes finite values while a continuous variabletake infinite values

1. Discrete variable

2. Continuous variable

3. Continuous variable

4. Discrete variable

Question14

=

Question15

Distributionis said to be a probability distribution if the following conditionsare met

1. The sum of all probabilities should total to 1

2. Individual probabilities should not be more than one

 1 2 3 4 5 TOTAL 0.37 0.12 0.14 0.07 0.03 1

Consideringthe conditions indicated above this is a probability distribution.The sum of all probabilities totals to 1 whereas the individualprobabilities are less than 1

 1 2 3 4 5 TOTAL 1.2 1.1 1.2 1.4 1.1 6

Thisdistribution is not a probability distribution. The sum of allprobabilities is greater than 1 and the individual expectations arebigger than one. It violates the earlier stated conditions.

Question16

 0 0.03 0 -1.09 1.1881 0 1 0.45 0.45 -0.09 0.0081 0.0036 2 0.15 0.3 0.91 0.8281 0.2484 3 0.06 0.18 1.91 3.6481 0.6567 4 0.04 0.16 2.91 8.4681 1.3549 Totals 1 1.09 2.2636

Question17

1. This does not represent a binomial distribution because there is no indication of repeated Bernoulli events. There are no two possible outcomes because the drugs are ordered from the most efficient to the least effective.

2. This is a binomial distribution because we find several repeated Bernoulli events. One painkiller is tested on 740 people, and it has two possible outcomes to every person. It is either effective or not effective.

Question18

Question19

=

nCx

10C010C110C210C310C410C5

Question20

1. Area is

2. Area is

Question21

Letbe a random variable representing the length of pregnancies

Therefore,standard deviation

(&gt 245)

Question22

Letbe a random variable representing the heights of women

Therefore,standard deviation

(62.0)

Question23

Yes,we can use a normal distribution to approximate the binomialdistribution. According to the Central Limit Theorem provided thesample size is sufficiently large any distribution tends to normality. Thus, in this case, the samplesize is greater than 30, and we can apply the CTL theorem toapproximate the binomial distribution using a normal distribution.

Bonusquestions

1. This is a Poisson distribution with

Giventhat

0.07

1. This is a geometric distribution with