the life span of a calculator manufactured by the intel corporation has a normal distribution with a mean of 54 months and a standard deviation of 8 months. The company gurantees that any calculator that start malfunctioning within 36 months of the purchase will be replaced by a new one. What is the probability that a randomly calculator will be replaced by a new one?
Z = (score-mean)/SD
Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportion/probability related to the Z score.
To find the probability that a randomly selected calculator will be replaced by a new one, we need to calculate the probability that a calculator malfunctions within 36 months of its purchase.
The life span of a calculator manufactured by Intel Corporation is normally distributed with a mean (μ) of 54 months and a standard deviation (σ) of 8 months.
We want to find the probability that a randomly selected calculator malfunctions within 36 months. Let's call this event A.
Step 1: Standardize the value of 36 using the z-score 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, x = 36, μ = 54, and σ = 8.
z = (36 - 54) / 8
z = -18 / 8
z = -2.25
Step 2: Look up the z-score in the standard normal distribution table or use a calculator or software to find the area under the standard normal curve to the left of -2.25.
Looking up the z-score of -2.25 in the standard normal distribution table, we find that the area to the left of -2.25 is approximately 0.0122.
Step 3: Calculate the probability of event A (calculator malfunctioning within 36 months) using the area we found in Step 2:
P(A) = 1 - area to the left of -2.25
P(A) = 1 - 0.0122
P(A) = 0.9878
Therefore, the probability that a randomly selected calculator will be replaced by a new one is approximately 0.9878 or 98.78%.