Respuesta :
Answer:
P(X > 1.05) = 1 - 0.8413 = 0.1587 = 15.87%.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 1, \sigma = 0.05[/tex]
Find P(X > 1.05).
This is 1 subtracted by the pvalue of Z when X = 1. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.05 - 1}{0.05}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
So P(X > 1.05) = 1 - 0.8413 = 0.1587 = 15.87%.
The value of P(x > 1.05) is 0.16
The given parameters are:
[tex]\mathbf{\sigma = 0.05}[/tex] --- the standard deviation
[tex]\mathbf{\mu = 1.000}[/tex] --- the mean
[tex]\mathbf{x = 1.05}[/tex] --- the sample reading
Start by calculating the z-score for x = 1.05 using:
[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]
So, we have:
[tex]\mathbf{z = \frac{1.05 - 1}{0.05}}[/tex]
[tex]\mathbf{z = 1}[/tex]
So, we have:
[tex]\mathbf{P(x > 1.05) = P(z > 1)}[/tex]
From z table of probabilities, we have:
[tex]\mathbf{P(z > 1) = 0.1587}[/tex]
This means that:
[tex]\mathbf{P(x > 1.05) = 0.1587}[/tex]
Approximate
[tex]\mathbf{P(x > 1.05) = 0.16}[/tex]
Hence, the value of P(x > 1.05) is 0.16
Read more about probabilities at:
https://brainly.com/question/11234923
