A company makes batteries with an average life span of 300 hours with a standard deviation of 75 hours. Assuming the distribution is approximated by a normal curve fine the probability that the battery will last .
Less than 250 hours
b. Between 225 and 375 hours
c. More than 400 hours
you can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
To find the probabilities, we need to standardize the values and use the Z-distribution table or a calculator that has a built-in normal distribution function. The formula to standardize a value is Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
In this case, the mean (μ) is 300 hours, and the standard deviation (σ) is 75 hours.
a. To find the probability that the battery will last less than 250 hours, we need to find the Z-value for 250 hours using the formula:
Z = (250 - 300) / 75 = -0.67
Using a Z-table or calculator, we can find the probability associated with the Z-value -0.67. The probability can be found to be approximately 0.2514 or 25.14%.
b. To find the probability that the battery will last between 225 and 375 hours, we need to standardize both values:
For 225 hours:
Z1 = (225 - 300) / 75 = -1.0
For 375 hours:
Z2 = (375 - 300) / 75 = 1.0
Now, we can find the probability associated with Z1 and subtract the probability associated with Z2 to find the probability between the two values. Using a Z-table or calculator, the probability will be approximately 0.6827 or 68.27%.
c. To find the probability that the battery will last more than 400 hours, we need to find the Z-value for 400 hours using the formula:
Z = (400 - 300) / 75 = 1.33
The probability associated with this Z-value can be found using a Z-table or calculator. The probability will be approximately 0.9088 or 90.88%.
Please note that these probabilities are approximations based on the assumption that the distribution is normal.