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.