Question: SAT verbal scores are normally distributed with a mean of 450 and a standard deviation of 120.


a) Use the Empirical Rule to find intervals centered at the mean of 450 that will include 68%, 95%, and 99.7% of all scores.

(b) Use the Empirical Rule to find what percent of scores lie between 210 and 570

(b) By symmetry, we have that 47.5% of the cases fall in (210, 450). Also, 34% fall in (450, 570). Therefore, 81.5% of the cases lie between 210 and 570.

Use the following to answer questions #13, 14, 15:

A local fire station receives an average of 0.50 rescue calls per day. Using software, Table 3 (Poisson probabilities), or the Poisson probability formula, find the following
probabilities for a randomly selected day:

1. Fewer than 2 calls will be received
2. 
   Between and including one or four calls will be received.

(More specifically, we use Poisson (1, 0.5, true) in Excel).

(b)We need to compute now

Use the following to answer #16, 17, and 18:

The distribution of salaries of elementary school teachers is approximately normal with mean m = $32000 and a standard deviation s = $5000.

a) If an individual teacher is selected at random, what is the probability that his or her salary is less than $36000?

(b) What is the cutoff salary for teachers who have salaries in the top 10%?

(c) If 35 teachers are randomly selected, what is the probability that their mean salary is between $31500 and $36000? Use the Central Limit Theorem.

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