Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. Using the standard deviation rule, what is the probability that a randomly chosen battery will last between 6.8 and 9.2 hours? 0.50 0.68 0.95 0.997
Question
Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. Using the standard deviation rule, what is the probability that a randomly chosen battery will last between 6.8 and 9.2 hours? 0.50 0.68 0.95 0.997
Solution
To solve this problem, we need to use the empirical rule (also known as the 68-95-99.7 rule) which states that for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean.
- About 95% falls within two standard deviations.
- About 99.7% falls within three standard deviations.
Given that the mean (μ) is 8 hours and the standard deviation (σ) is 1.2 hours, the range of 6.8 to 9.2 hours is within one standard deviation from the mean (8 - 1.2 = 6.8 and 8 + 1.2 = 9.2).
Therefore, according to the empirical rule, the probability that a randomly chosen battery will last between 6.8 and 9.2 hours is approximately 0.68 or 68%.
Similar Questions
The following histogram displays the distribution of battery life (in hours) for a certain battery model used in cell phones:Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. Using the standard deviation rule, what is the probability that a randomly chosen battery will last between 6.8 and 9.2 hours? 0.50 0.68 0.95 0.997
The rechargeable battery made by company A for E-bike had an average durability of 240 hours and a standard deviation of 20 hours after being fully charged. If a sample of 6 fully charged batteries is taken, find the probability that the sample mean exceeds 235 hours.a.0.2500b.0.7291c.1.000d.0.2709
The life of cell batteries is normally distributed with a mean of 92.3 hours and a standard deviation of 23.5 hours. What is the maximum time (in hours) that the worst 13% of batteries last? (2 dec pl )
A random sample of 15 batteries resulted in an average life of 280 hours with a standard deviation of 24 hours. Assume the battery life to be normally distributed and α = 0.05. Test the following hypothesis:H0: µ = 300 hoursH1: µ ≠ 300 hoursa.reject H0.b.There is no reason to believe that the battery life has changed.c.Accept the null hypothesis.d.Fail to reject the H0.
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians’ yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians exceeds $60,000?Multiple Choice0.15870.69150.30850.8413
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.