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

.

faster, im not sure why but i know it is faster

the square root of 16 is 4.

4*4 = 16