a study found that the means waiting time to see a physican at an outpatient clinic was 40 minutes with a standard deviation of 28 minutes. use excel to find each probability. a. what is the probability of more than an hours wait? B. less than 20 minutes? C. at least 10 minutes?
To find each probability, we need to use the standard normal distribution and the given mean and standard deviation. We will use Excel's functions to calculate these probabilities.
a. Probability of more than an hour wait:
To find the probability of waiting more than an hour, we need to find the area under the normal distribution curve to the right of 60 minutes (1 hour).
In Excel, you can use the formula "=1-NORM.DIST(x,mean,standard_dev,TRUE)" to find the probability to the right of the given value (x) in a normal distribution. Let's use this formula to calculate the probability.
Steps:
1. Open Excel and enter the following parameters:
- Mean: 40 (minutes)
- Standard Deviation: 28 (minutes)
- Value (x): 60 (minutes)
2. In an empty cell, enter the following formula:
"=1-NORM.DIST(60,40,28,TRUE)"
3. Press "Enter" to get the probability result.
The calculated probability is the probability of waiting more than an hour at the outpatient clinic.
b. Probability of less than 20 minutes wait:
To find the probability of waiting less than 20 minutes, we need to find the area under the normal distribution curve to the left of 20 minutes.
In Excel, you can use the formula "=NORM.DIST(x,mean,standard_dev,TRUE)" to find the probability to the left of the given value (x) in a normal distribution. Use this formula to calculate the probability.
Steps:
1. In an empty cell, enter the following formula:
"=NORM.DIST(20,40,28,TRUE)"
2. Press "Enter" to get the probability result.
The calculated probability is the probability of waiting less than 20 minutes at the outpatient clinic.
c. Probability of at least 10 minutes wait:
To find the probability of waiting at least 10 minutes, we need to find the area under the normal distribution curve to the right of 10 minutes.
In Excel, you can use the formula "=1-NORM.DIST(x,mean,standard_dev,TRUE)" to find the probability to the right of the given value (x) in a normal distribution. Use this formula to calculate the probability.
Steps:
1. In an empty cell, enter the following formula:
"=1-NORM.DIST(10,40,28,TRUE)"
2. Press "Enter" to get the probability result.
The calculated probability is the probability of waiting at least 10 minutes at the outpatient clinic.
To find the probabilities using Excel, we can make use of the Z-Score formula along with the standard normal distribution.
First, we need to calculate the Z-Score, which measures the number of standard deviations a data point is from the mean. The formula for Z-Score is:
Z = (X - μ) / σ
Where:
X is the given value
μ is the mean
σ is the standard deviation
a. To find the probability of more than an hour's wait (i.e., more than 60 minutes):
1. Calculate the Z-Score using the given values:
Z = (60 - 40) / 28 = 20 / 28 = 0.71
2. In Excel, use the following formula to find the probability for a Z-Score:
=1 - NORMDIST(Z, 0, 1, TRUE)
Substituting the value of Z into the formula:
=1 - NORMDIST(0.71, 0, 1, TRUE)
This will give you the probability of waiting more than an hour.
b. To find the probability of less than 20 minutes:
1. Calculate the Z-Score using the given values:
Z = (20 - 40) / 28 = -20 / 28 = -0.71
2. In Excel, use the following formula to find the probability for a Z-Score:
=NORMDIST(Z, 0, 1, TRUE)
Substituting the value of Z into the formula:
=NORMDIST(-0.71, 0, 1, TRUE)
This will give you the probability of waiting less than 20 minutes.
c. To find the probability of at least 10 minutes:
1. Calculate the Z-Score using the given values:
Z = (10 - 40) / 28 = -30 / 28 = -1.07
2. In Excel, use the following formula to find the probability for a Z-Score:
=1 - NORMDIST(Z, 0, 1, TRUE)
Substituting the value of Z into the formula:
=1 - NORMDIST(-1.07, 0, 1, TRUE)
This will give you the probability of waiting at least 10 minutes.
Using these formulas, you can input the values into Excel to find the desired probabilities.
I don't know how to use Excel for this.
Z = (score - mean)/SD
See the Help for Excel for Z test.