The time spent by students working on a project is a normal random variable with parameters μ= 12 and = 4. a. what is the probability that the amount of the time spent on a project is less than 14 hours? b. what is the probability that the amount of the time spent on a project is greater than 8 hours?

a) The probability is 0.19146.

b) The probability is 0.15866.

Step-by-step explanation:

a) In this problem we have a random variable X with normal distribution, and its parameters are μ = 12 and σ = 4. The variable X stands for the amount of time that the students spend in a project. With this, our problem is to find the probability that X is less than 14. So,

.

Recall that the tables we have are made to calculate probabilities with standardized normal variables, this means that its mean is 0 and its standard deviation is 1. This can be done considering the variable .

Now, we look down the rows to find 0.5 and then across the columns to 0.00 which yield a probability of 0.19146.

b) In this case we want to calculate . We follow an analogue reasoning:

Now we use that where Y is a random variable. Then,

.

But,

.

Now we substitute this last value and get

.

Again, we look into the table and found that

.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

details

step-by-step explanation: