The time required to travel downtown at am on Monday morning is known to be normally distrubted with a mean of 40 minutes and a standard deviation of 5 minute what is the probability that it will take less than 40 minutes?
If it is normally distributed, mean = median = mode. Look at the definition of each of these terms.
.20
0.53
To find the probability that it will take less than 40 minutes to travel downtown on Monday morning, we need to use the information given about the distribution (mean and standard deviation) and apply the concept of the standard normal distribution.
The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. By transforming our problem into the standard normal distribution, we can use a Z-table or a statistical software to find the desired probability.
To transform our problem, we need to calculate the z-score, which tells us how many standard deviations an observation is from the mean. The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value we want to find the probability for (in this case, 40 minutes)
- μ is the mean of the distribution (40 minutes in this case)
- σ is the standard deviation of the distribution (5 minutes in this case)
Substituting the values into the formula, we have:
z = (40 - 40) / 5 = 0
Since the z-score is 0, we can directly look up the probability associated with it on a standard normal distribution table or in statistical software. The probability associated with a z-score of 0 is 0.5.
Therefore, the probability that it will take less than 40 minutes to travel downtown on Monday morning is 0.5 or 50%.