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# probability distributions

1. Find the value of (a) in the following discrete probability distribution:
X -2 0 2
P(x): a 0.35 0.25

2. A binomial distribution is based on n=25 and p=0.1. Find the probability that x =1.

3 A production process produces parts with weights that are normally distributed with a mean of 1.75 ounces and a standard deviation of 0.15 ounces. If specifications call for weights between 1.50 and 2.25 ounces, what percent are not within specifications?

4 If the scores on a test were normally distributed with a mean equal to 500 and a standard deviation equal to 100, what test score would produce a z score equal to 1.5?

5 A certain intersection has a stop light that some residents feel is inappropriately placed. They estimate that 25% of all cars through the intersection do not stop for a red light. If this is true, how many in a sample of 300 cars encountering a red light would one expect to see not stop? What is the probability that less than 20% of the 300 cars would be observed running a red light?

#### Solution Preview

1. Sum of Probabilities should be 1.
<br> So a + .35+ .25 = 1
<br> or a = .4
<br>
<br>2. P(X=1) = (n C x)*(p^x)*(1-p)^n-x
<br> = 25C1* .1^1*.9^24
<br> = .199
<br>
<br>3. Mean(M) = 1.75
<br> Std Dev = .15
<br> Lower Limit = 1.5
<br> Upper Limit = ...

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