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Ksivusya [100]
3 years ago
12

Let X denote the number of flaws along a 100-m reel of magnetic tape (an integer-valued variable). Suppose Zdenote the number of

flaws along a 100-m reel of magnetic tape (an integer-valued variable). Suppose has approximately a normal distribution with μ =25 and σ = 5 . Use the continuity correction to calculate the probability that the number of flaws is Between 20 and 30, inclusive.
At most 30. Less than 30.
Mathematics
1 answer:
Lemur [1.5K]3 years ago
3 0

Answer:

a) P(20 \leq X \leq 30) = P(20-0.5 \leq X \leq 30+0.5)

P(19.5 \leq X \leq 30.5) = P(\frac{19.5-25}{5} \leq Z \leq \frac{30.5 -25}{5})=P(-1.1 \leq Z \leq 1.1)

And we can find this probability like this:

P(-1.1 \leq Z \leq 1.1)= P(Z\leq 1.1) -P(Z\leq -1.1) = 0.864-0.136= 0.728

b) P(X \leq 30)= P(X

And using the z score we got:

P(X

c) P(X

And if we use the continuity correction we got:

P(X

Step-by-step explanation:

Previous concepts

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".  

Continuity correction means that we need to add and subtract 0.5 before standardizing the value specified.

Part a

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

X \sim N(25,5)  

Where \mu=25 and \sigma=5

Part a

For this case we want to find this probability:

P(20 \leq X \leq 30) = P(20-0.5 \leq X \leq 30+0.5)

And if we use the z score given by:

z =\frac{x-\mu}{\sigma}

We got this:

P(19.5 \leq X \leq 30.5) = P(\frac{19.5-25}{5} \leq Z \leq \frac{30.5 -25}{5})=P(-1.1 \leq Z \leq 1.1)

And we can find this probability like this:

P(-1.1 \leq Z \leq 1.1)= P(Z\leq 1.1) -P(Z\leq -1.1) = 0.864-0.136= 0.728

Part b

For this case we want this probability:

P(X \leq 30)

And if we use the continuity correction we got:

P(X \leq 30)= P(X

And using the z score we got:

P(X

Part c

For this case we want this probability:

P(X

And if we use the continuity correction we got:

P(X

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<u>Answer: </u>

Required five terms of sequence are 19 , 12 , 5 , -2 and -9 .

<u> Solution: </u>

Need to find the five terms of the sequence.

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= f(2) = f(1) – 7    ------(1)

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On substituting the given value of f(2) in eq (1) we get

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Substituting x = 3 ,  

f(3) = f(3-1) – 7  

= f(2) – 7  

= 12 – 7  

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Using given recursive rule and calculated  value of f(3) calculating f(4)

Substituting x = 4,  

f(4) = f(4-1) – 7  

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Substituting x = 5,  

f(5) = f(5-1) – 7  

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Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:
mars1129 [50]

Answer:

A = (x + 15)(x + 10) − 5

Step-by-step explanation:

(x+15)(x+10)-5=A would be a solution

To make this easier, let's assign x a value. Let's say 3.

(3+15)(3+10)-5=A

(18)(13)-5=A

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Now with this, we put x in the answer choice and the answer that gives an area of 229 is correct.

A. A=(3+20)(3+10)+12=(23)(13)+12=299+12=311 <u>Answer A is wrong.</u>

B. A=(3+20)(3+10)-12=(23)(13)-12=299-12=287 <u>Answer B is wrong.</u>

C. A=(3+26)(3+15)=(29)(18)=522 <u>Answer C is wrong.</u>

D. A=(3+14)(3+8)=(17)(11)=187 <u>Answer D is wrong.</u>

It's either I'm wrong or the answer choices are wrong.

New answer choices!

A. A=(3+20)(3+11)

=(23)(14)=322 Answer A is wrong.

B. A=(3+15)(3+10)+5

=(18)(13)+5=234+5=239  Answer B is wrong.

C. A=(3+15)(3+10)−5

=(18)(13)-5=234-5=229 Answer C is correct.

D. A=(3+9)(3+10)=(12)(13)=156 <u>Answer D is wrong.</u>

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