Final answer:
To find the probability that a randomly selected terminal will last more than 5 years, we can use the normal distribution and standardize the value to find the cumulative probability. Accessing a standard normal distribution table or using a calculator, we find that the probability is approximately 0.0668. Therefore, the correct answer is (a) 0.0668.
Step-by-step explanation:
To solve this problem, we can convert the given mean and standard deviation from years to months. The mean of 4 years is equal to 48 months, and the standard deviation of 8 months remains the same. Since we want to find the probability that a randomly selected terminal will last more than 5 years, which is equivalent to 60 months, we need to find the probability that a terminal will last more than 60 months.
Using the normal distribution, we can find this probability by standardizing the value of 60 using the formula z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation. In this case, the standardized value is z = (60 - 48) / 8 = 1.5.
Next, we can use a standard normal distribution table or a calculator to find the cumulative probability to the left of 1.5. The area to the left of 1.5 represents the probability that a terminal will last less than or equal to 60 months, so we subtract this value from 1 to find the probability that a terminal will last more than 60 months. Using a standard normal distribution table or a calculator, we find that the probability is approximately 0.0668. Therefore, the correct answer is (a) 0.0668.
The probability that a randomly selected computer terminal will last more than 5 years, given a mean life expectancy of 4 years and a standard deviation of 8 months, is approximately 0.0668.
The question involves calculating the probability that a computer terminal will last more than 5 years given that the life expectancy is normally distributed with a mean of 4 years and a standard deviation of 8 months (which is 2/3 years). To solve this, we need to calculate the z-score for the value of 5 years and then find the corresponding probability using the standard normal distribution table or calculator.
To calculate the z-score:
Z = (X - μ) / σ
Where X is the value we are interested in (5 years), μ is the mean (4 years), and σ is the standard deviation (2/3 years). So,
Z = (5 - 4) / (2/3) = 1.5
Using a standard normal distribution table or a calculator, we find the probability that a z-score is greater than 1.5, which typically involves looking up the z-score and subtracting from 1 because tables and calculators often provide the probability that a value is less than a certain z-score.
Based on the standard normal distribution, the probability (p-value) that a computer terminal lasts more than 5 years is approximately 0.0668. Therefore, the correct answer is (a) 0.0668.