Amachine manufactures parts whose diameters vary according to the normal distribution with mean 40.150 mm and standard deviation 0.003mm. an inspector measures a random sample of 4 parts. the probability that the average (x-bar) diameter of these 4 parts is less than 40.148 mm is about

The probability that the average (x-bar) diameter of these 4 parts is less than 40.148 mm is about 0.09176 or 9.2%

Step-by-step explanation:

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

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".  

Let X the random variable that represent the diameters of a population, and for this case we know the distribution for X is given by:

Where and

They select a sample if size n=4, by the central limit theorem the distribution for the sample mean is given by:

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 use this formula we got this:

The probability that the average (x-bar) diameter of these 4 parts is less than 40.148 mm is about 0.09176 or 9.2%

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

∡ eia and ∡ kij are congruent

step-by-step explanation: