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Answer:
c) P(270≤x≤280)=0.572
d) P(x=280)=0.091
Step-by-step explanation:
The population of bearings have a proportion p=0.90 of satisfactory thickness.
The shipments will be treated as random samples, of size n=500, taken out of the population of bearings.
As the sample size is big, we will model the amount of satisfactory bearings per shipment as a normally distributed variable (if the sample was small, a binomial distirbution would be more precise and appropiate).
The mean of this distribution will be:
The standard deviation will be:
We can calculate the probability that a shipment is acceptable (at least 440 bearings meet the specification) calculating the z-score for X=440 and then the probability of this z-score:
Now, we have to create a new sampling distribution for the shipments. The size is n=300 and p=0.932.
The mean of this sampling distribution is:
The standard deviation will be:
c) The probability that between 270 and 280 out of 300 shipments are acceptable can be calculated with the z-score and using the continuity factor, as this is modeled as a continuos variable:
d) The probability that 280 out of 300 shipments are acceptable can be calculated using again the continuity factor correction:
The equation of the transformation of the exponential function <em>y</em> = 2ˣ in the form <em>y</em> = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is <em>y</em> = (-2)·2ˣ + 3
<h3>What is an exponential equation?</h3>An exponential equation is an equation that has exponents that consists of variables.
The given equation is <em>y</em> = 2ˣ
The equation for the transformation is; <em>y</em> = A·2ˣ + k
The points on the graphs are;
(0, 1), (1, -1) and (2, -5)
Plugging the <em>x </em>and <em>y</em>-values to find the value <em>A</em> and <em>k</em> gives the following simultaneous equations;
When <em>x</em> = 0, <em>y</em> = 1, therefore;
1 = A·2⁰ + k = A + k
1 = A + k...(1)
When <em>x</em> = 1, <em>y</em> = -1, which gives;
-1 = A·2¹ + k
-1 = 2·A + k...(2)
Subtracting equation (1) from equation (2) gives;
-1 - 1 = 2·A - A + k - k
-2 = A
1 = A + k, therefore;
1 = -2 + k
k = 2 + 1 = 3
k = 3
Which gives;
y = -2·2ˣ + 3 = 3 - 2·2ˣ
Learn more about the solutions to simultaneous equations here:
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