Find z such that 87.9% of the standard normal curve lies to the left of z. (round your answer to two decimal places.) z =
2 answers:
Answer with explanation:
It is given that, 87.9% of the standard normal curve lies to the left of z.
Z (87.9%)
Total Area under Z curve =1
Now, we have to find area left of, (Z value =87.9%=88%)=0.88
⇒Area to left of Z curve , when, (Z value =87.9%=88%)=0.88
= 0.81 (Approximation to two decimal Places)
You might be interested in
Answer:
And we can find this probability on this way:
We expect around 68.27% between the two scores provided.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
We expect around 68.27% between the two scores provided.