The MPG for a certain compact car is normally distributed with a mean of 31 and a standard deviation of 0.8. what is the probability that the MPG for a randomly selected compact car would be less than 32?
To find the probability that the MPG for a randomly selected compact car is less than 32, we need to calculate the z-score and then use the standard normal distribution table.
The z-score formula is:
Z = (X - μ) / σ
Where:
X = The value we want to find the probability for (32 in this case)
μ = The mean of the distribution (31 in this case)
σ = The standard deviation of the distribution (0.8 in this case)
Using the formula:
Z = (32 - 31) / 0.8
Z = 1 / 0.8
Z = 1.25
Now, we can use the standard normal distribution table or a calculator to find the probability associated with the z-score of 1.25. Looking up the z-score of 1.25 in the table, we find that the probability is approximately 0.8944.
Therefore, the probability that the MPG for a randomly selected compact car is less than 32 is approximately 0.8944, or 89.44%.
To find the probability that the MPG for a randomly selected compact car would be less than 32, we can use the concept of the standard normal distribution.
First, we need to calculate the z-score for the given value of 32. The z-score measures the number of standard deviations a data point is from the mean in a normal distribution. The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
- x is the value you want to find the probability for (32 in this case)
- μ is the mean of the MPG distribution (31 in this case)
- σ is the standard deviation of the MPG distribution (0.8 in this case)
Plugging in the values, we get:
z = (32 - 31) / 0.8 = 1.25
Next, we need to find the probability corresponding to this z-score. We can use a standard normal distribution table (also known as the z-table) to find this probability.
Looking up the z-score of 1.25 in the z-table, we find that the probability corresponding to this z-score is approximately 0.8944.
Therefore, the probability that the MPG for a randomly selected compact car would be less than 32 is approximately 0.8944, or 89.44%.
89.4%
I used the computation tool at
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html
Enter the mean, the std. dev. and the limits, and hit "Enter"