en a normal distribution with µ =4 and σ =2, what is the probability that 5% of the values are less than what X values? Between what two X values (symmetrically distributed around the mean) are 95 % of the values? Instructions: Draw the normal curve Insert the mean and standard deviation Label the area of 5% under the curve, and the area of 95% under the curv Use Z to solve the unknown X values ( lower X and Upper X)
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!
Given a
- 5% of the values are less than what X values?
- Between what two X values (symmetrically distributed around the
mean ) are 95 % of the values?
Instructions:
- Draw the normal curve
- Insert the mean and standard deviation
- Label the area of 5% under the curve, and the area of 95% under the curv
- Use Z to solve the unknown X values ( lower X and Upper X)
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