# Math Help - Finding Probabilities and Hypothesis testing

1. ## Finding Probabilities and Hypothesis testing

I've ground to a halt on these last 3 questions on my midterm review sheet. Any help I could get figuring these out would be appreciated.

Let’s suppose there is a variable that measures how anxious people are about taking a test. We’ll call it the TAI (Test Anxiety Index). It ranges from 0 (totally relaxed) to 100 (sweating bullets) and is normally distributed with a mean of 80 and variance of 25.
a) What is the probability that someone from this distribution has a TAI less than 68? b) What is the probability that someone from this distribution has a TAI greater than 85? c) What is the probability that someone from this distribution has a TAI less then 93?
For this one, I think the way to do it is to square root 25 to get 5, and then divide (80-68)/5 which gives you 2.4. I then look up 2.4 on a Z table to get .4918. Is this the correct way of doing this?

When I first arrived at SCU, I attended a new faculty orientation and I was surprised to hear a Psychology professor report that her students conducted a study of SCU students and found that the average number of drinks they consumed on any given weekend was 11 drinks. Based on my neighbors’ activities, I had assumed it was much more than that. So I decided to research it myself.
I collect a random sample of 100 SCU students and ask them how many drinks they consumed over the previous weekend. I then calculate the mean in my sample and find that they drank 11.6 drinks on average that weekend.
Assuming that the variance in the population of SCU students is 9, conduct a hypothesis test using this information. Make sure to explicitly set out both the null and alternative hypotheses, explaining your reasoning for choosing them and conclude with your decision about whether or not you can reject the null hypothesis.
Let’s say we are interested in the changing patterns of political ideology in America. I have a hunch that America is becoming less conservative. Based on 2004 ANES data, the average political ideology score was 4.44 (on a scale of 1 to 7, with 7 being very conservative). Based on a random sample of 1100 respondents, the 2008 ANES has an average political ideology score of 4.14. Assuming that the population distribution in 2008 had a variance of 25, conduct a hypothesis test using the z-distribution, being sure to state your null and alternative hypotheses.
These second two I don't even know where to begin with.

2. $P(X<68)=P\left( {X-80\over 5}<{68-80\over 5}\right)$

$P(Z<-2.4)$

I have no idea how you arrived at .4918.
Maybe you looked up -.24