Math Help - stuck on a couple problems

1. stuck on a couple problems

1. Assume that Z is a normal random variable with mean 0 and variance 1.

P(Z-1)=?
P(Z?)=0.20

If someone can show either one of these I will be able to work the other I am confident.

2. A random variable has a normal distribution with μ=62.4. Find its standard deviation if the probability is 0.20 that it will take on a value greater than 79.2.

everytime I work this one out I get a negative SD. Basically hat i did was take the Z score from the table forthe 20% which was -.96. Then did the z= x-u/SD and re arranged to find it. 79.2-62.4/-.96 is a negative SD and not possible. I dont see what I am doing wrong.

3. A safety supervisor feels that 30% of all industrial accidents in his plant are caused by failure of employees to follow instructions. If this failure is correct, find approximately the probability that among 84 industrial accidents in his plant anywhere from 20 to 30 (inclusive) will be due to failure of employees to follow instructions.

Way lost on this one.

Thanks in advance guys, just a navy fella trying to get through some college and remember some of the basics.

JC

2. Re: stuck on a couple problems

You can find Z values or inverse Z values from a table or online calculator.

$P(Z\geq -1 ) = 1- 0.68-.16= \cdots$ from the 68%/95%/99.7% rule

3. Re: stuck on a couple problems

Originally Posted by woopigg
1. Assume that Z is a normal random variable with mean 0 and variance 1.

P(Z-1)=?
P(Z?)=0.20

If someone can show either one of these I will be able to work the other I am confident.

2. A random variable has a normal distribution with μ=62.4. Find its standard deviation if the probability is 0.20 that it will take on a value greater than 79.2.

everytime I work this one out I get a negative SD. Basically hat i did was take the Z score from the table forthe 20% which was -.96. Then did the z= x-u/SD and re arranged to find it. 79.2-62.4/-.96 is a negative SD and not possible.
You are going the wrong way. If the probability x is greater than 79.2 is 20%, then the probability x is less than 79.2- which is what the table gives- is 80%. Repeat your calcuations using 80%, not 20%.
(The reason you were getting a negative value is that you were trying to say the probability of being LESS than a number LARGER than the mean is less than 50% and that is impossible.)

I dont see what I am doing wrong.

3. A safety supervisor feels that 30% of all industrial accidents in his plant are caused by failure of employees to follow instructions. If this failure is correct, find approximately the probability that among 84 industrial accidents in his plant anywhere from 20 to 30 (inclusive) will be due to failure of employees to follow instructions.

Way lost on this one.

Thanks in advance guys, just a navy fella trying to get through some college and remember some of the basics.

JC