Question

Question 1 (5 points)

An industrial oven has a mean operating temperature of 450 degrees Fahrenheit
with a standard deviation of 25 degrees. Given this information what is the
probability that the oven will have a temperature between 434 degrees and 450
degrees? (Assume a normal distribution)

A.) 0.331008
B.) 0.208126
C.) 0.238914
D.) 0.125228
E.) 0.060270

Answer 1

0.238914 is the probability that the oven will have a temperature between 434 degrees and 450 degrees.

Option C

Explanation:

Here we have , An industrial oven has a mean operating temperature of 450 degrees Fahrenheit with a standard deviation of 25 degrees. We need to find what is the probability that the oven will have a temperature between 434 degrees and 450 degrees . Let's find out:

Step 1: Sketch the curve.

The probability that 434<X<450 is equal to the blue area under the curve.

Step 2:

Since μ=450 and σ=25 we have:

P ( 434<X<450 )=P ( 434−450< X−μ<450−450 )

⇒ P ( 434−450/25< X−μ/σ < 450−450/25)

Since Z = x−μ/σ , 434−450 25 = −0.64 and 450−450/25 = 0 we have:

P ( 434<X<450 )=P ( −0.64<Z<0 )

Step 3: Use the standard normal table to conclude that:

P ( −0.64<Z<0 )=0.2389

Therefore , Correct option C) 0.238914 .