Answer: 0.0142
Step-by-step explanation:
Given : The mean height of women in a country (ages 20 - 29) is 64.2 inches.
i.e. [tex]\mu=64.2[/tex]
Also, [tex]\sigma=2.58[/tex]
Sample size : n= 50
Let x denotes the height of women.
Then, the probability that the mean height for the sample is greater than 65 inches :-
[tex]P(x>65)=1-P(x\leq 65)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{65-64.2}{\dfrac{2.58}{\sqrt{50}}})\\\\=1-P(z\leq2.193)\ \ [\because z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9858463\ \ [\text{By using z-value table or calculator}]\\\\=0.0141537\approx0.0142[/tex]
Hence, the the probability that the mean height for the sample is greater than 65 inches = 0.0142
