Below is a graph of a normal distribution with mean =-3 and standard deviation o=4. The shaded region represents the probability of obtaining a value from this distribution that is less than 3. 03- 0.2- 01- Shade the corresponding region under the standard normal density curve below.
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!
![Below is a graph of a normal distribution with mean \( \mu = -3 \) and standard deviation \( \sigma = 4 \). The shaded region represents the probability of obtaining a value from this distribution that is less than 3.
*[Insert Graph]
*Graph Description: The graph is a bell curve centered at \( x = -3 \) with a standard deviation of 4. The x-axis ranges from approximately -15 to 9, and the y-axis shows the probability density with divisions up to 0.05. The section of the curve from the far left up to \( x = 3 \) is shaded in blue, indicating the cumulative probability of obtaining a value less than 3.
Shade the corresponding region under the standard normal density curve below.
*[Insert Graph]
*Graph Description: The graph is a standard normal distribution curve centered at \( z = 0 \) with a standard deviation of 1. The x-axis ranges from approximately -5 to 5, and the y-axis shows the probability density with divisions up to 0.4. The cusp of the curve is centered at 0, forming the characteristic bell shape of the standard normal distribution.
Explanation
The task involves understanding the concept of standard normal distribution and how to translate probabilities from a normal distribution to a standard normal distribution.
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