The life span of a calculator has a normal distribution with a mean of 60 months and a standard deviation of 5 months. If a calculator is randomly selected, find the probability that the calculator has a life span of.
(1) more than 50 months
(2) between 4 years and 6 years.
http://davidmlane.com/hyperstat/z_table.html
Using a TI-84 calculator, find the area under the standard normal curve to the right of the following -values. Round the answers to four decimal places.
Part 1 of 4
The area to the right of is
.
Part 2 of 4
The area to the right of is
.
Part 3 of 4
The area to the right of is
To find the probability in these cases, we will use the z-score formula and the standard normal distribution. The z-score formula is given by:
z = (x - μ) / σ
Where:
z is the z-score,
x is the value we want to find the probability for,
μ is the mean, and
σ is the standard deviation.
Based on the given information:
Mean (μ) = 60 months
Standard Deviation (σ) = 5 months
Let's calculate the probability for each case:
(1) Probability of the calculator having a life span more than 50 months:
To find this probability, we need to calculate the z-score for 50 months and then find the area under the curve to the right of the z-score.
z = (x - μ) / σ
z = (50 - 60) / 5
z = -2
Now, we need to find the area to the right of the z-score -2 using the standard normal distribution table or a calculator. The area to the right of -2 represents the probability of the calculator having a life span more than 50 months.
(2) Probability of the calculator having a life span between 4 years (48 months) and 6 years (72 months):
To find this probability, we need to calculate the z-scores for both 48 months and 72 months and then find the area under the curve between these two z-scores.
For 48 months:
z1 = (48 - 60) / 5
z1 = -2.4
For 72 months:
z2 = (72 - 60) / 5
z2 = 2.4
Now, we need to find the area between z1 and z2 using the standard normal distribution table or a calculator. The area between these two z-scores represents the probability of the calculator having a life span between 4 years and 6 years.
Please note that the exact probabilities will depend on the specific z-table or calculator used.