Respuesta :
Answer:
The probability that the actual event is less than 6.5 inches is 0.9999.
Step-by-step explanation:
We are given that you have determined that for this gage you have a standard error of 30%.
For a precipitation event of 5 inches, we have to find the probability that the actual event is less than 6.5 inches.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean precipitation event = 5 inches
standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = 0.30
Now, the probability that the actual event is less than 6.5 inches is given by = P(X < 6.5 inches)
P(X < 6.5 inches) = P( [tex]\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{6.5-5}{0.30}[/tex] ) = P(Z < 5) = 0.9999
The above probability is calculated by looking at the value of x = 5 but in the z table the last value of x is given as 4.40 so we take the area of that value only which has an area of 0.9999.
