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In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A

vredina [299]

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:

$\mu_s=np=500*0.90=450$

The standard deviation will be:

$\sigma_s=\sqrt{np(1-p)}=\sqrt{500*0.90*0.10}=\sqrt{45}=6.7$

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:

$z=(x-\mu_s)/\sigma_s=(440-450)/6.7=-10/6.7=-1.49\\\\P(z>-1.49)=0.932$

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:

$\mu=np=300*0.932=279.6$

The standard deviation will be:

$\sigma=\sqrt{np(1-p)}=\sqrt{300*0.932*0.068}=\sqrt{19}=4.36$

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:

$P(270\leq x\leq280)=P(269.5$

d) The probability that 280 out of 300 shipments are acceptable can be calculated using again the continuity factor correction:

$P(X=280)=P(279.5$

8 0

3 years ago

I need help ASAP Please

const2013 [10]

Answer:

oh god

Step-by-step explanation:

8 0

3 years ago

Ftmdnydngdngd fbfdjj

levacccp [35]

Answer:

The above triangle is an isosceles triangle....

Reason

As we can see AB and DE are parallel to each other

As angle ABC is 80 degree

Therefore BCE is too 80 degree (as they both are alternate to each others)

Hence angle DCB is a 50 degree because in the straight DCE we have angle BCE as 80 degree and Angle ACD as 50 degree

Since a straight line has 180 degree therefore the remaining angle ACB is 50 degree(180-80-50)

Now in triangle BAC. Angle C is 50 degree and Angle B is 80 degree, since the total angle of a triangle is 180 degree therefore A is 50 degree that is angle BAC is 50 degree(180-50-80) .

Hence here we see that two opposite sides have same angle that is the reason its a ISOSCELES triangle

Answer BY AN INDIAN

THANK YOU

7 0

3 years ago

Given f(x) = 5x - 7 and g(x) = x² - 3, find f(f(2)).

sveta [45]

Step-by-step explanation:

Given f(x) = 5x - 7 and g(x) = x² - 3, find f(f(2))

4 0

3 years ago

5(10k + 1) + 2(2 +8k) Choose 1 ansvar

MrRa [10]

Answer:

50k + 5 + 4 + 16k

66k + 9

Step-by-step explanation:

4 0

3 years ago