About % of the area under the curve of the standard normal distribution is outside the interval Z = (-1.07,1.07) (or beyond 1.07 standard deviations of the mean). Please show your answer to 2 decimal places.
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!
About % of the area under the curve of the standard
![### Understanding the Standard Normal Distribution
#### Explanation and Question
The diagram above depicts a bell-shaped curve representing the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1.
On the x-axis, you can see various values, specifically: -3, -2, -1, 0, 1, 2, and 3. These values represent the number of standard deviations away from the mean.
The blue shaded regions in the graph indicate the areas outside the interval Z = (-1.07, 1.07). This means we are interested in the proportion of the distribution that lies beyond -1.07 standard deviations to the left and 1.07 standard deviations to the right of the mean.
**Question:**
*About [_____] % of the area under the curve of the standard normal distribution is outside the interval Z = (-1.07, 1.07) (or beyond 1.07 standard deviations of the mean). Please show your answer to 2 decimal places.*
Note: Use the standard normal distribution table or relevant statistical software to determine this percentage.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f7cf5db-cb40-4137-92b2-0f52d9b26804%2Ff3a8d5fa-1b2b-497e-aa79-122ba06ccc05%2Fzq8rxoul_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
