the letter "T" makes up an estimated 8% of a certain language. Assume this still correct. A random sample of 1000 letters is taken from a randomly selected, large book and the t's are counted. find the approximate probability that the random sample of 1000 letters will contain 7.4% or fewer t's

Question

Mathematics

Khalil Petersen

26 February, 09:24

the letter "T" makes up an estimated 8% of a certain language. Assume this still correct. A random sample of 1000 letters is taken from a randomly selected, large book and the t's are counted. find the approximate probability that the random sample of 1000 letters will contain 7.4% or fewer t's

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Answers (1)

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Jose Arias · Answer 1

0.242

Step-by-step explanation:

p = 0.08, q = 1 - p = 0.92, and n = 1000.

The mean and standard deviation are:

μ = p = 0.08

σ = √ (pq/n) = 0.00858

The z score is:

z = (x - μ) / σ = - 0.70

Using a calculator or z score table, the probability is:

P (Z < - 0.70) = 0.242