Question

11A research

team conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)

(a) at least one tie is too tight

(b) more than two ties are too tight

(c) no tie is too tight

(d) at least 18 ties are not too tights

 

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Question

Suppose x has a distribution

with a mean of 50 and a standard deviation of 3. Random samples of size n = 36

 are drawn.

(a) Describe the x distribution

 and compute the mean and standard deviation of the distribution. 

x

 has 

—Select—

a normal

an approximately normal

a geometric

a binomial

a Poisson

an unknown

 distribution with mean μ_x = 

 and standard deviation σ_x =  .

(b) Find the z value corresponding to x = 51.

z = 

(c) Find P(x < 51).

 (Round your answer to four decimal places.) 

P(x < 51) = 

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 51? Explain. 

No, it would not be unusual because more than 5% of all such samples have means less than 51.

Yes, it would be unusual because less than 5% of all such samples have means less than 51.

No, it would not be unusual because less than 5% of all such samples have means less than 51.

Yes, it would be unusual because more than 5% of all such samples have means less than 51.

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