Given that X∼N(42.9,97.1). Find the probability that a

sarahmuthoni080

sarahmuthoni080

Answered question

2022-05-06

Given that XN(42.9,97.1). Find the probability that a randomly chosen value from this population is less than 86. Find

 

z

p(x less than or equal to 86

Answer & Explanation

xleb123

xleb123

Skilled2023-05-04Added 181 answers

We are given that X follows a normal distribution with mean μ=42.9 and variance σ2=97.1. We need to find the probability that a randomly chosen value from this population is less than 86, and also find the z-score for this probability.
To find the probability that X is less than 86, we need to standardize 86 using the formula:
z=xμσ
Substituting the given values, we get:
z=8642.997.12.78
Now, we need to find the probability that X is less than or equal to 86. This can be calculated using the standard normal distribution table or calculator. From the table, we find that the probability of Z2.78 is approximately 0.9974.
Therefore, the probability that a randomly chosen value from this population is less than 86 is approximately 0.9974, and the z-score for this probability is 2.78.
In summary, the solutions are:
- P(X<86)0.9974
- z=2.78 for P(X86)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?