Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.
3.7
To find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot, we need to calculate the area under the normal distribution curve between these two values.
Here's how you can do it:
1. Convert the given data into a standard normal distribution, where the mean (μ) is 5 minutes and the standard deviation (σ) is 2 minutes. To standardize the values, use the formula: z = (x - μ) / σ, where x is the value we are interested in.
2. Standardize the lower value of 2 minutes:
z1 = (2 - 5) / 2 = -1.5
3. Standardize the upper value of 6 minutes:
z2 = (6 - 5) / 2 = 0.5
4. Look up the corresponding probabilities in the standard normal distribution table. The probability associated with z1 is P(z < -1.5) and the probability associated with z2 is P(z < 0.5).
5. Since we want the probability between 2 and 6 minutes, which is the area between z1 and z2, we subtract P(z < -1.5) from P(z < 0.5).
6. Use the standard normal distribution table or a calculator to find the probabilities. The resulting probability should be in decimal form.
Alternatively, you can use a calculator or a statistical software package that provides functions to calculate the area under the normal distribution curve, such as the cumulative distribution function (CDF) of the standard normal distribution. By inputting the standardized values, you can directly obtain the probability between these values without using the table.
Please note that the standard normal distribution table gives the probabilities to the left of the given z-value, so you may need to use the complement (1 - P(z)) if you need the probability to the right of the z-value.