Respuesta :
Answer:
d. 2.28%
Step-by-step explanation:
Problems of normally distributed samples are 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 = 0.3, \sigma = 0.01[/tex]
What percentage of bolts will have a diameter greater than 0.32 inches?
This is 1 subtracted by the pvalue of Z when X = 0.32. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.32 - 0.3}{0.01}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228 = 2.28%
So the correct answer is:
d. 2.28%
Answer: option D is the correct answer.
Step-by-step explanation:
Since the diameters of bolts produced by a certain machine are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = diameter of bolts
µ = mean diameter
σ = standard deviation
From the information given,
µ = 0.3 inches
σ = 0.01 inches
We want to find the probability bolts that will have a diameter greater than 0.32 inches. It is expressed as
P(x > 0.32) = 1 - P(x ≤ 0.32)
For x = 0.32,
z = (0.32 - 0.3)/0.01 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.9773
P(x > 0.32) = 1 - 0.9733. = 0.0228
The percentage of bolts will have a diameter greater than 0.32 inches is
0.0228 × 100 = 2.28%
