Statistics and Probability Answers

Suppose that a continuous random variable 𝑋 has a probability density function

given by

𝑓(𝑥) = {

0 if 𝑥 ≤ 0

2𝑥

𝑅2

if 0 < 𝑥 ≤ 𝑅

0 if 𝑥 > 𝑅

Find the variance of 𝑋.

How to explain for mean, variance and standard deviation ? The question need me to explain all those 3 in one sentence but I don't know how to relate it

The probability that a smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.

The probability that neither sound an alarm in the presence of smoke

In a large lot of electric bulbs to the mean life and standardization of a bust 36 hours and 19 hours respectively does a sample of 625 bulb is chosen it is found that the mean life and standard deviation of bulbs in the sample 355 hours and 19 hours respectively can we conclude that the sample is drawn from a given population test at 5% level of significance

A bag contains 4 blue balls and 8 red balls If two balls are drawn from bag at random,what is the probability that one ball is blue and the other is red

Below is a 5-item true or false test. Determine whether the statement is true or

false. Write T if the statement is true and F if false on the blank provided before the

number.

1. The area under a normal curve is 100.

2. The area under the curve corresponds to all probabilities of X.

3. The mean of a standard normal curve is 0.

4. The normal curve is bell-shaped and is symmetrical about its center.

5. The curve is determined by the standard deviation of the distribution.

Below is a 5-item true or false test. Determine whether the statement is true or false. Write T if the

statement is true and F if false on the blank provided before each number.

1. Probability value is a number from 0 to 1.

2. Probability value is a number from −1 to 1.

3. Finding the area of a region is the same as finding the probability. associated with that region.

4. The probability that the z-score falls at most 𝑧 = −1 is equal to the probability of that the z-score falls less than 𝑧 = −1.

5. It is possible to have a negative probability.

Below is a 5- item true or false test. Determine whether the statement is true or false. Write T if the statement is true and F if false on the blank provided before each number.

1. The z-score measures how many standard deviation a given value is above or below the mean.

2. A negative z-score indicates that the score or value is above the mean.

3. If a z-score is equal to −2.05, it is 2.05 standard deviations below the mean.

4. A positive z-score indicates that the score or value is below the mean,

5. If a z-score is 0, it is on the mean.

Find the corresponding area between 𝑧 = 0 and each of the following.

1. z = 0.85

2. z = 1.27

3. z = 2.86

4. z = −1.05

5. z = −2.96

Using the z-table, find the corresponding area between 𝑧 = 0 and each of the following:

1. z = 0.92

2. z = 1.29

3. z = 2.73

4. z = −0.50

5. z = −2.98