12. Evaluate the function rule for the given value.y = 4×2* for x = -6
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Answer:
At 12.10% of days fewer lifeguards will be provided.
Step-by-step explanation:
We are given that the daily high temperatures in a vacation resort city are approximately Normal, with a mean temperature of 75 degrees Fahrenheit and a standard deviation of 6 degrees.
Let X = <u><em>the daily high temperatures in a vacation resort city</em></u>
So, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean temperature = 75 degrees Fahrenheit
= standard deviation = 6 degrees Fahrenheit
Now, the percentage of days at which fewer lifeguards will be provided is given by = P(X 68°)
P(X 68°) = P(
) = P(Z
-1.17) = 1 - P(Z < 1.17)
= 1 - 0.879 = <u>0.121 or 12.10% </u>
The above probability is calculated by looking at the value of x = 1.17 in the z-table which has an area of 0.8790.
Hence, at 12.10% of days fewer lifeguards will be provided.