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

  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.

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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

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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.

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

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step-by-step explanation: