a.  Given   P(A)  =  0.2,   P(B)  =0.3 and  P(A and B ) = 0.1              Find   (i)  P ( A or B ) =                        ( ii ) Are the events A, B independent ? Justify.

Q: Compute the mean of each sample and the mean of the sample means.

A: The sample mean for each sample can be calculated as Mean = Sum of observations/Sample size.

Q: Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is…

A:

Q: Which of the following conclusions is most likely based on a valid survey? 24.1% of the students at…

A:

Q: The relationship between the mean and the median for the N(0, 1) distribution is: a. mean>median…

A:

Q: Determine the size of each sample. nE = (Type integers or decimals. Do not round.)

A: The size of males is, nM=174+370=544 Thus, the size of males is 544.

Q: A businesswoman is considering whether to open a coffee shop in a local shopping center. Before…

A: a) For the given data values, The point estimate of the population mean is 21.3886, from the excel…

Q: Which hypothesis test needs to be employed here? z test one-sample t test Odependent t test…

A: It is given that the data of the relationship between age and golf performance.

Q: A biology professor claims that, on the average, 15% of her students get a grade of A, 25% get a B,…

A: The number of categories k is 5.

Q: If variances are unequal, you pool the variances

A: State and explain whether the given statement is true or false.

Q: The number of text messages sent and the number of phone calls made in a sample of 100 students…

A:

Q: Determine the mean value of x for the following: X: 0, 1, 2, 3, 4 P(x): .4, .1, .1, .1, .3

A: We want to find the mean  E(X)= ?

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.