Use technology to solve the following problem: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean $\mu = 37$ and standard deviation $\sigma = 5$ . What Proportion of tires have lifetimes between 33 and 48 thousand miles?
A) 1.1980
B) 0.7742
C) 3.0000
D) 0.2258

Question

Quizplus · Accepted Answer

We can solve this problem using normal distribution and Z-score. 
First, we need to standardize the values of 33 and 48 using the formula: 
Z = (X - μ) / σ 
For X = 33, Z = (33 - 37) / 5 = -0.8 
For X = 48, Z = (48 - 37) / 5 = 2.2 
Then, we can look up the area under the standard normal curve between -0.8 and 2.2 using a Z-table or a calculator. 
Using a calculator, we get: 
P(-0.8 < Z < 2.2) = 0.7742 
Therefore, the proportion of tires with lifetimes between 33 and 48 thousand miles is 0.7742 or approximately 77.42%. The answer is B.

Use Technology to Solve the Following Problem: the Lifetime of a Certain