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A paint company claims their paint will be completely dry within 45 minutes after application. Recently, customers have complained drying times are longer than the claimed 45 minutes. A consumer advocate group takes a random sample of 25 paint specimens and records their drying times. The average drying time x is 52. Consider dryng time, for all test specimens, to be normally distributed with ? = 6.


Suppose the claimed drying time is true, that is ? = 45 minutes, what is the probability of observing a sample mean of x = 52 or greater from a sample size of 25? (Round your answer to four decimal places.)

Respuesta :

Answer:

The probability of observing a sample mean of x = 52 or greater from a sample size of 25 is 0.0000026

Step-by-step explanation:

Mean = [tex]\mu = 45[/tex]

Population standard deviation =[tex]\sigma = 6[/tex]

Sample size = n =25

Sample mean = [tex]\bar{x} = 52[/tex]

We are supposed to find  the probability of observing a sample mean of x = 52 or greater from a sample size of 25 i.e.[tex]P(x\geq 52)[/tex]

[tex]Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\Z=\frac{52-45}{\frac{6}{\sqrt{25}}}[/tex]

Z=5.83

P(Z<52)=0.9999974

[tex]P(Z\geq 52)=1-P(z<52)=1-0.9999974=0.0000026[/tex]

Hence  the probability of observing a sample mean of x = 52 or greater from a sample size of 25 is 0.0000026

JKaur4154

Answer:

the probability of observing a sample mean of x = 52 or greater from a sample size of 25 is 0.0000026

Step-by-step explanation:

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