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A recent report in a women magazine stated that the average age for women to marry in the United States is now 25 years of age, and that the standard deviation is assumed to be 3.2 years. A sample of 50 U.S. women is randomly selected. Find the probability that the sample mean age for 50 randomly selected women to marry is at most 24 years

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JeanaShupp

Answer:  0.0136

Step-by-step explanation:

Given : Mean : [tex]\mu=\ 25[/tex]

Standard deviation : [tex]\sigma= 3.2[/tex]

Sample size : [tex]n=50[/tex]

The formula to calculate the z-score :-

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x = 24

[tex]z=\dfrac{24-25}{\dfrac{3.2}{\sqrt{50}}}=-2.20970869121\aprox-2.21[/tex]

The P-value =[tex]P(z\leq24)=0.0135526\approx0.0136[/tex]

Hence, the probability that the sample mean age for 50 randomly selected women to marry is at most 24 years = 0.0136

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