The lifetime of a SuperTough AAA battery is normally distributed with mean of 28.5 hours and standard deviation of 5.3 hours. For a battery selected at random, what is the probability that the lifetime will be 25 hours or less?
a. 0.7454
b. 0.6604
c. 0.2546
d. 0.3396
http://davidmlane.com/hyperstat/z_table.html
answer c. check it with the applet.
To find the probability that the lifetime of the battery will be 25 hours or less, we need to calculate the area under the normal distribution curve up to 25 hours.
First, we need to calculate the z-score for 25 hours:
z = (X - μ) / σ
where,
X = 25 (lifetime in hours)
μ = 28.5 (mean)
σ = 5.3 (standard deviation)
z = (25 - 28.5) / 5.3
z = -0.6604 (approx)
Next, we need to look up the z-score in the standard normal distribution table or use a calculator to find the area under the curve.
The area to the left of a z-score of -0.6604 is approximately 0.2546.
Therefore, the probability that the lifetime of the battery will be 25 hours or less is approximately 0.2546.
So, the correct answer is c. 0.2546.
To find the probability that the lifetime of a SuperTough AAA battery is 25 hours or less, we need to calculate the area under the normal distribution curve up to 25 hours.
First, we need to standardize the value of 25 using the formula:
Z = (X - μ) / σ
where:
Z is the standardized value
X is the value we want to find the probability for (25 hours)
μ is the mean of the distribution (28.5 hours)
σ is the standard deviation of the distribution (5.3 hours)
Plugging in the values gives us:
Z = (25 - 28.5) / 5.3 ≈ -0.6604
Next, we need to find the cumulative probability up to the z-score of -0.6604 using a standard normal distribution table or a calculator.
Looking up the z-score -0.6604 in a standard normal distribution table or using a calculator, we find that the cumulative probability is approximately 0.2546.
Therefore, the probability that the lifetime of a SuperTough AAA battery is 25 hours or less is approximately 0.2546.
So the answer is c. 0.2546.