Find the mean and standard deviation

Reference no: EM132591916

Question 1: One of the most profitable items at Aix Auto Security Shop is the remote starting system. Let x he the number of such systems installed on a given day at this shop. The following table lists the frequency distribution of x for the past RI days.

x 1 2 3 4 5

f 8 20 24 16 12

a. Construct a probability distribution table for the number of remote starting systems installed on a given day.

x P(x)

1 ____

2 ____

3 ____

4 ____

5 ____

Choose the graph of the probability distribution.

b. Are the probabilities listed it the table of part a exact or approximate probabilities of the various outcomes?
Exact probabilities

Approximate probabilities

c. Find the following probabilities.
I. P (x = 5)
P (x = 5) = ____

II. P (x ≥ 3)

P (x ≥ 3) = _____

III. P(2 ≤ x ≤ 4)

P(2 ≤ x ≤ 4) =

Iv. P (x < 5)

P (x < 5) =

Question 2:

Find the mean and standard deviation for the following probability distribution.

x	p(x)
0	0.17
1	0.27
2	0.47
3	0.09

Enter the exact answer for the mean and round the standard deviation to three decimal places.
Mean =
Standard deviation =

Question 3:
Let x be a discrete random variable that possesses a binomial distribution. Using the binomial formula, rind the following probability. P(x = 4) for n = 8 and p = 0.4
Round your answer to four decimal places.
P(x = 4) =
the absolute tolerance is +1-0.0001

Question 4:
Let x be a discrete random variable that possesses a binomial distribution with is = 5 and p = 0.73. What are the mean and standard deviation of this probability distribution?
Round your answers to three decimal places, if required.
Mean =
Standard deviation =

Question 5:

In a group of 18 persons, 3 are left-handed. Suppose that two persons are randomly selected from this group. Let x denote the number of left-handed persons in this sample. Cheese the correct probability distribution of x. (Hint: Note that the draws are made without replacement from a small population. Hence, the probabilities of outcomes do not remain constant for each draw.)

Question 6:

The following table gives the probability distribution of a discrete random variable x.

0 1 2 3 4 5 6

P(x) 0,11 0.18 0.29 0.15 0.11 0.09 0.07

Find the probability that assumes a value greater than 2.
P=
exact number, no tolerance

Question 7:

The following table gives the probability distribution of a discrete random variable x.

x	0	1	2	3	4	5	6
P(x)	0.11	0.19	0.27	0.14	0.11	0.07	0.11

Find P(1 ≤ x ≤ 4).
P(1 ≤ x ≤ 4)
exact number, no tolerance

Question 8:

Find the mean and standard deviation for the following probability distribution.

x P (x)

0 0.17

1 0.3

2 0.38

3 0.15

Enter the exact answer for the mean and round the standard deviation to three decimal places.
Mean =
Standard deviation =

Question 9:

One of the most profitable items at Al, Auto Security Shop is the remote starting system. Let x be the number of such systems installed on a given day at this shop. The following table lists the frequency distribution of x for the past 80 days.

x 1 2 3 4 5
f 8 20 24 16 12

a. Construct a probability distribution table for the number of remote starting systems installed on a given day.

Choose the graph of the probability distribution.

b. Are the probabilities listed in the table of part a exact or approximate probabilities of the various outcomes?
Exact probabilities
Approximate probabilities

c. Find the following probabilities.
I. P (x = 3)
P (x = 3) =

II. P (x ≥ 2)

P(x ≥ 2)=

III. P(2 ≤ x ≤ 5)

P(2 ≤ x ≤ 5) =

iv. P (x < 5)

P(x < 5) =

Question 10:

Let x be a discrete random variable that possesses a binomial distribution. Using the binomial formula, find the following probability.
P(x = 5) for = 8 and p = 0.3
Round your answer to four decimal places.
P(x = 5) =
the absolute tolerance is +1-0.0001

Question 11:

Let x be a discrete random variable that possesses a binomial distribution with en = 5 and p = 0.72. What are the mean and standard deviation of this probability distribution?
Round your answers to three decimal places, if required.
Mean
Standard deviation

Question 12:
According to a survey conducted at the local DMV, 53% of drivers who drive to work stated that they regularly exceed the posted speed limit on their way to work. Suppose that this result is true for the population of (Myers who drive to work. A random sample of 11 drivers who drive to work is selected. Use the binomial probabilities table (Table I of Appendix B) or technology to find to 3 decimal places the probability that the number of drivers in this sample of 11 who regularly exceed the posted speed limit on their way to work is
a. at most 6 Probability =
b. 5 to 9
Probability =
c. at least 6
Probability =

Question 13:

The following table lists certain values of x and their probabilities. Verify whether or not it represents a valid probability distribution.

x	p(x)
0	0.36
1	0.30
2	0.20
3	0.10

a valid probability distribution.

Question 14:

x	p(x)
0	0.10
1	0.15
2	0.10
3	0.65

The following table lists certain values of x and their probabilities. Verify whether or not it represents a valid probability distribution.

Question 15:
An office supply company conducted a survey before marketing a new paper shredder designed for one use. In the survey, 8011 of people who used the shredder were satisfied with It. because of this high acceptance rate, the company Beaded to market the new shredder. Assume that 80% of all people who use it will be satisfied. On a certain day, seven customers bought this shredder.
a. Let x denote the number of customers in this sample of seven who will be satisfied with this shredder. Using the binomial probabilities table, obtain the probability distribution of z and 911 in the table below.
Round your answers to four dedmal places.

Fill the mean and standard deviation of x.

Enter the exact answer tar the Mean, and round the Standard deviation to three decimal places_
μ = customers
σ = customers

Choose the graph of the probability distribution of x.

b. Using the probability distribution of part a, find the probability that exactly seven of the seven customers will be satisfied. Round the answer to four decimal places.

P(exactly seven).

Attachment:- assigment.rar

Reference no: EM132591916

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