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vladimir2022 [97]
3 years ago
10

The letter​ "t" makes up an estimated 10​% of a certain language. Assume this is still correct. A random sample of 500 letters i

s taken from a randomly​ selected, large book and the​ t's are counted. Find the approximate probability that the random sample of 500 letters will contain 9.1​% or fewer​ t's.

Mathematics
1 answer:
Andrew [12]3 years ago
6 0

Answer:

  0.2755

Step-by-step explanation:

We intend to make use of the normal approximation to the binomial distribution.

First we'll check to see if that approximation is applicable.

For p=10% and sample size n = 500, we have ...

  pn = 0.10(500) = 50

This value is greater than 5, so the approximation is valid.

__

The mean of the distribution we'll use as a model is ...

  µ = p·n = 0.10(500)

  µ = 50

The standard deviation for our model is ...

  σ = √((1-p)µ) = √(0.9·50) = √45

  σ ≈ 6.708204

__

A continuity correction can be applied to better approximate the binomial distribution. We want p(t ≤ 9.1%) = p(t ≤ 45.5). For our lookup, we will add 0.5 to this limit, and find p(t ≤ 46).

The attached calculator shows the probability of fewer than 45.5 t's in the sample is about 0.2755.

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Step-by-step explanation:

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Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant​ criteria?Tem
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Answer:

B. No, this distribution does not appear to be normal

Step-by-step explanation:

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CCSS Math 7
Andre45 [30]

Answer:

1.

a = 112

b = 68

c = 68

2.

a = 127

3.

a=35

b=40

c=35

d=70

4.

a= 30

b=70

c = 30

d=70

e = 130

I'll help you with the rest later

Step-by-step explanation:

a = 112 because of allied angles rule

b and c = 68 because of angles at a point

360-112-112 ÷2

2. a = 127 because of angles on a straight line rule.

180-38-15

3. d= 70, vertically opposite angle

using angles on a straight line, 180 - 70 - 40 ÷ 2

we now have the two angles and because they are vertically opposite a and c = 35

b = 40 because of vertically opposite angles

4. a=30 because 90-70

since a=30, take 90 - 30 to get b, 70

d= 70, vertically opposite angles

e = 130 because a+b+c, vertically opposite angles

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2 years ago
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