To calculate how many laptops will fail before the warranty expires, we need to find the number of laptops that have a lifespan of less than or equal to 2 years.
We can use the normal distribution to estimate the number of laptops that will fail before the warranty expires. We can assume that the laptop lifespan follows a normal distribution with a mean of 3.8 years and a standard deviation of 0.58 years.
First, we need to calculate the z-score for the value x = 2 years:
z = (x - mu) / sigma = (2 - 3.8) / 0.58 = -3.10
where mu is the mean lifespan of the laptop and sigma is the standard deviation.
We can then use a standard normal distribution table or a calculator to find the probability that a normal random variable is less than or equal to the z-score of -3.10. This probability is approximately 0.001.
Therefore, the proportion of laptops that will fail before the warranty expires is approximately 0.001.
To find the number of laptops that will fail before the warranty expires out of 5000 laptops sold, we can multiply the proportion by the total number of laptops:
Number of laptops that will fail before the warranty expires = 0.001 * 5000 = 5
Therefore, we can expect that 5 laptops out of 5000 sold will fail before the warranty expires.