(a) P(z < zo) = 0.834 Zo (b) P(-zo < z < zo) = 0.25 Zo = (c) P(-zo < z < z0) = 0.2936 Zo =
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!
Find the value of the standard normal random variable ?, called ?0 such that:
![The image contains a set of statistical probability expressions, each accompanied by a blank space intended for solving the associated z-score value. These are common exercises in statistics courses to help students understand probabilities associated with the standard normal distribution.
Here is the transcription of the expressions:
(a) \( P(z \leq z_0) = 0.834 \)
- \( z_0 = \) [Blank space for solution]
(b) \( P(-z_0 \leq z \leq z_0) = 0.25 \)
- \( z_0 = \) [Blank space for solution]
(c) \( P(-z_0 \leq z \leq z_0) = 0.2936 \)
- \( z_0 = \) [Blank space for solution]
(d) \( P(z \geq z_0) = 0.0326 \)
- \( z_0 = \) [Blank space for solution]
(e) \( P(-z_0 \leq z \leq 0) = 0.0969 \)
- \( z_0 = \) [Blank space for solution]
(f) \( P(-1.48 \leq z \leq z_0) = 0.5905 \)
- \( z_0 = \) [Blank space for solution]
Each part requires the determination of the z-score (\( z_0 \)) that meets the specified probability condition. These exercises are useful for understanding and interpreting areas under the normal distribution curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa29210f1-c509-4cc5-a424-b61c622bd259%2Feb3c0fc9-d526-4c9a-894d-f45db154f1d4%2Fpba5an_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
