Answer :
Answer:
If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than 466.37 grams
Step-by-step explanation:
Mean = [tex]\mu = 464[/tex]
Standard deviation =[tex]\sigma = 6[/tex]
We are supposed to find If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than how many grams i.e.P(X>x)=0.02
The mean weight is in the highest 2%, you want to go to a z-table and find the z-score that where the area to the left of the curve is closest to 0.98.
n = 27
Refer the z -table
P(Z>x)=2.06
[tex]\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}=2.06\\\frac{x-464}{\frac{6}{\sqrt{27}}}=2.06\\x-464=2.06 \times \frac{6}{\sqrt{27}}\\x=(2.06 \times \frac{6}{\sqrt{27}})+464\\x=466.37[/tex]
So, If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than 466.37 grams