Answer: 0.031
Step-by-step explanation:
As considering the given information, we have
[tex]\mu=80[/tex]
[tex]\sigma=28[/tex]
n= 75
Let x be the random variable that represents the price of all routers.
We assume that the price of all routers are normally distributed.
Z-score corresponding to x=74 will be :-
[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z=\dfrac{74-80}{\dfrac{28}{\sqrt{75}}}\\\\=-1.8557687224\approx-1.86[/tex]
Using z-value table,
P-value = P(x ≤ -1.86)=1-P(x≤ 1.86)=1-0.9685572=0.0314428≈0.031
Hence, the required probability = 0.031
