The ages of 180 patients in ONA last Sunday are normally distributed with μ=25 yrs old and σ=8.5 yrs. What percent is older than 30 yrs old? What percent is younger than 35 yrs old? How many are younger than 10 yrs old? How many are between 12 yrs old and 28 yrs old? How many are between 32 yrs old and 40 yrs old?
3 years ago
Answered By Leonardo F
Since the population of patients is normally distributed, we can use the normal distribution table to answer these questions. First, let's recall the formula for the reduced variable in the normal distribution z:
z = (x - mean)/(std deviation)
To find out the z for 30 years old, we do:
z = (30 - 25)/8.5 = 0.59
Looking at the table for the area to the left of this value of z:
Area = 0.722
This means that 72.2% of the data is below 30 years old. So, 27.8% is above 30 years old.
Doing the same for 35 years old:
z = (35 - 25)/8.5 = 1.18
Looking at the table for the area to the left of this value of z:
Area = 0.880
This means that 88.0% of the data is younger than 35 years old.
Doing the same for 10 years old:
z = (10 - 25)/8.5 = -1.76
Looking at the table for the area to the left of this value of z:
Area = 0.039
This means that 3.9% of the data is younger than 10 years old.
For 12 and 28 years old:
z = (12 - 25)/8.5 = -1.53
z = (28 - 25)/8.5 = 0.35
If we do the area to the left of 28 minus the area to the left of 12, we have:
0.638 - 0.063 = 0.575
This means that 57.5% of the data is between 12 and 28 years old.
For 32 and 40 years old:
z = (32 - 25)/8.5 = 0.82
z = (40 - 25)/8.5 = 1.76
If we do the area to the left of 40 minus the area to the left of 32, we have:
0.961- 0.795 = 0.166
This means that 16.6% of the data is between 32 and 40 years old.
3 years ago
Answered By Leonardo F
Since the population of patients is normally distributed, we can use the normal distribution table to answer these questions. First, let's recall the formula for the reduced variable in the normal distribution z:
z = (x - mean)/(std deviation)
To find out the z for 30 years old, we do:
z = (30 - 25)/8.5 = 0.59
Looking at the table for the area to the left of this value of z:
Area = 0.722
This means that 72.2% of the data is below 30 years old. So, 27.8% is above 30 years old.
Doing the same for 35 years old:
z = (35 - 25)/8.5 = 1.18
Looking at the table for the area to the left of this value of z:
Area = 0.880
This means that 88.0% of the data is younger than 35 years old.
Doing the same for 10 years old:
z = (10 - 25)/8.5 = -1.76
Looking at the table for the area to the left of this value of z:
Area = 0.039
This means that 3.9% of the data is younger than 10 years old.
For 12 and 28 years old:
z = (12 - 25)/8.5 = -1.53
z = (28 - 25)/8.5 = 0.35
If we do the area to the left of 28 minus the area to the left of 12, we have:
0.638 - 0.063 = 0.575
This means that 57.5% of the data is between 12 and 28 years old.
For 32 and 40 years old:
z = (32 - 25)/8.5 = 0.82
z = (40 - 25)/8.5 = 1.76
If we do the area to the left of 40 minus the area to the left of 32, we have:
0.961- 0.795 = 0.166
This means that 16.6% of the data is between 32 and 40 years old.