stat question help please!?

Question

4. A group of FSU psychologists examined the effects of alcohol on the reactions of people to a threat (Journal of Abnormal Psychology, Vol. 107, 1998). After obtaining a blood alcohol level (BAL) of at least .015, experimental subjects were placed in a room and threatened with electric shocks. Using sophisticated equipment to monitor the subjects’ eye movements, the startle response (measured in milliseconds) was recorded for each subject. The mean and standard deviation of the startle responses were 37.9 and 12.4, respectively. Assume that the startle response x for a person with a BAL of at least .015 is approximately normally distributed.



1. Find the probability that x is between 40 and 50 milliseconds.





2. Find the probability that x is less than 30 milliseconds.





3. Within what limits (upper and lower bounds) would you expect x to fall 95% of the time?

Answer 1

Dear jason n,

You need to use tables for the normal distribution or a computing device which will provide them. Tables are usually standardized for a normal distribution having mean 0 and standard deviation 1. To standardize you calculate z = (value - mean) / standard deviation. For example, for a startle response of 40 ms you have
z = (40 - 37.9) / 12.4
= 2.1 / 12.4
= 0.16935 (to five decimal places).
Looking up this value in a standardized normal table then gives
0.56724, which is the area under the normal probability density curve to the left of z. In other words, it is the probability that a startle response is less than 40 ms.

1. You can find the probability that x is less than 50 ms in the same manner as described in the example above (0.83542). Once you do that, you can subtract the probability of x < 40 ms from the probability of x < 50 ms to find the probability that x is between 40 ms and 50 ms, which is 0.26818 (to five decimal places).

2. This is even easier than the first question. Just follow the example and you should get 0.26203 (to five decimal places).

3. If you want an interval that is symmetric with respect to the mean, then I would expect x to be between 13.59645 ms and 62.20355 ms 95% of the time. However, there are infinite such intervals which are not symmetric about the mean, with the two extreme cases being the interval bounded by negative infinity and 58.29618 ms, and the interval bounded by 17.50382 ms and positive infinity.