Answer :
Part a: The probability that a given battery will last between 2.3 and 3.6 years is 80.41%.
Part b: The probability that a given battery will last longer than 24 months is 97.72%.
What is meant by the normal distribution?
- A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder slacken off symmetrically toward any extreme.
For the given question,
The data for the storage battery are-
- Mean μ = 3.0 years.
- Standard deviation σ = 0.5 years.
Part a: The probability that a given battery will last between 2.3 and 3.6 years.
Find z score for x = 2.3 years.
z(2.3) = (x - μ )/σ
Put the values,
z(2.3) = (2.3 - 3.0)/0.5
z(2.3) = -1.4
Use negative z score table;
P(z = -1.4) = 0.0808
Similarly, for x = 3.6
z = (3.6 - 3)/0.5
z = 1.2
Use positive z table;
z = 0.8849
P(2.3<x<3.6) = 0.8849 - 0.0808
P(2.3<x<3.6) = 0.8041
Thus, the probability that a given battery will last between 2.3 and 3.6 years is 80.41%.
Part b: The probability that a given battery will last longer than 24 months = 2 years.
x = 2 years
z (2) = ( 2 - 3.0 )/ 0.5
z = 2
P(x > 2) = 0.9772
Thus, the probability that a given battery will last longer than 24 months is 97.72%.
To know more about the normal distribution, here
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