Statistics and Probability Answers

What do you call a random variable whose possible outcomes are on a continuous scale?

Supply the table with the corresponding random variable and/or the possible values of the random variable for each experiment.

Experiment | Random Variable (𝑿) |

Possible values (𝒙) for the Random Variable

example 1. Contacting 10 customers | Number of customers who placed a complaint | 0, 1, 2, 3, 4, 5

2. Inspection of shipment of 100 laptops |_blank_ | 0, 1, 2, … , 99, 100

3. Filling a bottle of water (maximum of 500 𝑚𝐿) |_blank_| 0 ≤ 𝑥 ≤ 500

4. Testing of new chemical

process | The temperature when the desired reaction takes place (minimum of 40 ˚𝐶; maximum of 90˚ 𝐶) | _blank_

5. Selling an automobile |_blank_| 0 if male; 1 if female

Two of the five (5) foreign automobiles from an overseas shipment have slight paint blemishes. If an agency receives three (3) of these automobiles at random, list the elements of the sample space 𝑆 using the letters B and N for “blemished” and “non-blemished”, respectively. For each sample point, assign a value 𝑥 of the random variable 𝑋 representing the number of automobiles purchased by the agency with

paint blemishes. Hint: There are eight (8) elements in the sample space.

Classify the following random variables as discrete or continuous.

1. The number of cellphone units of GHI Mobile Company sold on a given day

2. The number of correct answers in a 50-item multiple choice test

3. The number of nonproductive hours in an eight-hour workday

4. The length of life (in hours) of a light bulb 5 . The number of vehicular accidents each year in Cainta, Rizal

The probability that Melcom Company will survive for the next 10 years is 0.75 the probability that Life Company will survive for the next 10 years is 0.80. What is the probability that:

(i) both will survive for the next 10 years

(ii) neither will survive for the next 10 years

On the basis of 5 years of data, the following probability function for a company weekly demand for wool was:

Amount (kg) 2500 3500 4500 5500

Probability 0.35 0.45 0.20 0.05

What was the expected weekly demand for wool based on the distribution?

a)   A company has taken a ballot of its workforce, asking them to choose between two alternative new schemes (A and B) for claiming travelling expenses. 60% of the workforce support scheme A, while 50% of these owning a car. If only 30% of those who support scheme B own a car, calculate the probability that if a worker is chosen at random, he will be:

    i.       a car owner

  ii.       a car owning, scheme A supporter

 iii.       a car owner, given that he supports scheme A

 iv.       a scheme A supporter, given that he owns a car

a)   Two vacuum cleaner salesmen A and B must each make two calls per day, one in the morning and one in the afternoon. A has a probability 0.4 of selling a cleaner on any call, while B (a novice) has a probability 0.1 of a sale. A works independently of B and, for each salesman, morning and afternoon results are independent of each other.

Find the probability that, in one day:

    i.       A sells 2 cleaners

   i.       A sells just one cleaner

  ii.       B makes at least one sale

 iii.       Between them, A and B make exactly one sale

The Head of the Math Department announced that the mean score of Grade 9 students in the first periodic examination in Mathematics was 89 and the standard deviation was 12. One student who believed that the mean score was less than this, randomly selected 34 students and computed their mean score. She obtained a mean score of 85. At 0.01 level of significance, test the student’s belief.

A research was conducted in 2017 at the Tema Port to find the ages of cars imported into

the country. According to the research, 10% of the cars imported were less than one-year-

old. Assuming this result holds true for the current period for all cars imported into the

country.

Find the probability that in a random sample of 5 cars at the Tema Port

(i) exactly 3 are less than one-year-old.

(ii) exactly 2 are less than one-year-old.

(iii) none is less than one-year-old

(iv) Find the mean and standard deviation of the distribution if a random

Sample of 200 cars were selected at Tema Port