In 2017, the entire fleet of light-duty vehicles sold in the United States by each manufacturer must emit an average of no more than 86 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000 miles of driving) of the vehicle. NOX +NMOG emissions over the useful life for one car model vary Normally with mean 82 mg/mi and standard deviation 5 mg/mi

(a) What is the probability that a single car of this model emits more than 86 mg/mi of NOX +NMOG? (Enter your answer rounded to four decimal places.)

probability:

(b) A company has 25 cars of this model in its fleet. What is the probability that the average NOX NMOG level cars is above 86 mg/mi? (Enter your answer rounded to four decimal places.)

probability:

a) 0.2119 = 21.19% probability that a single car of this model emits more than 86 mg/mi of NOX +NMOG

b) 0% probability that the average NOX NMOG level cars is above 86 mg/mi

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sample means with size n can be approximated to a normal distribution with mean and standard deviation

In this problem, we have that:

(a) What is the probability that a single car of this model emits more than 86 mg/mi of NOX +NMOG?

This is 1 subtracted by the pvalue of Z when X = 86. So

has a pvalue of 0.7881

1 - 0.7881 = 0.2119

0.2119 = 21.19% probability that a single car of this model emits more than 86 mg/mi of NOX +NMOG

(b) A company has 25 cars of this model in its fleet. What is the probability that the average NOX NMOG level cars is above 86 mg/mi?

Now we have that

This is 1 subtracted by the pvalue of Z when X = 86. So

By the Central Limit Theorem

has a pvalue of 0.99998.

1-99998 = 0.00002

0% probability that the average NOX NMOG level cars is above 86 mg/mi

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where,

here given table is,

price ($), x   :           18         23       25       29       30       33

pairs sold, y :         16         13         10       8         6       2

so, ,   ,   ,

and   ,

thus, slop of the given line is,

⇒  

⇒   ≈ 33