The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

a. 47.72%
b. 97.72%
c. 37.45%
d. 2.28%
e. 4.56%

d. 2.28%

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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:

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

has a pvalue of 0.9772

1 - 0.9772 = 0.0228 = 2.28%

So the correct answer is:

d. 2.28%

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%

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

a

step-by-step explanation: