Question

Software companies work hard to produce software without bugs. A particular company claims that 88% of the software it produces is bug free. A random sample of size 500 software programs was considered.

Calculate the mean of the sampling distribution of the sample proportion.

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Calculate the standard deviation of the sampling distribution of the sample proportion. (Round your answer to four decimal places.)

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Calculate the probability of obtaining a sample proportion of 418 or fewer bug-free software programs out of 500 if the company's claim is true. (Round your answer to four decimal places.)

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Answer 1

Solution

Given that,

p = 0.88

1 - p = 1 - 0.88 = 0.12

n = 500

= p = 0.88

=  [p ( 1 - p ) / n] =   [(0.88 * 0.12) / 500] = 0.0145

P( < 0.836)

= P[( - ) / < (0.836 - 0.88) / 0.0145]

= P(z < - 3.03 )

Using z table,

= 0.4880