Directions: Draw the normal curve and shade in the specific region. Show formulas used and the substitution. Assume that the salaries of the elementary school teachers in the United States with a mean of 31,000 dollars and a standard of 3000 dollars. a. If 100 teachers are randomly selected, find the probability that their mean salary is greater than 31,500 dollars. b. If 120 teachers are selected, what is the probability that their mean salary is greater than 31,500? So as the sample size increases, what happens to the probability value. c. If the 120 teachers are randomly selected what is the probability that their mean salary is between 31,200 to 31,500
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Directions: Draw the normal curve and shade in the specific region. Show formulas used and the substitution.
Assume that the salaries of the elementary school teachers in the United States with a
a. If 100 teachers are randomly selected, find the
b. If 120 teachers are selected, what is the probability that their mean salary is greater than 31,500? So as the
c. If the 120 teachers are randomly selected what is the probability that their mean salary is between 31,200 to 31,500
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