I need help with algebra 2 questions.

Question

A standard deviation test has a mean of 50 and a standard deviation of 4. Fin the probability of test scores in the following ranges.
1. between 42 and 58
2. below 46
3. between 46 and 54
The amount of coffee in a can has a mean of 350g and a standard deviation of 4g.
4. What percent of cans have less than 338g of coffee?
5. What is the probability that a can has between 342 and 350 g.
6. What is the probability that a can has less than 342 g or more than 346 g of coffee?

Answer 1

z = (x - mean)/stddev

 

1)    Prob( 42 < x < 58) = Prob(x<58) - Prob(x<42) =  Prob( z < (58-50)/4) - Prob ( z < (42-50)/4)

                                                                                 Prob( z < -2) - Prob( z < -2)

                                                                                    0.9772 - 0.0228 = 0.9554

 

2) Prob( x<46) = Prob( z < (46-50)/4) = Prob ( z < -1) =0.1587

 

The third part is done the same way as #1. I will leave it for you to do.