Consider the approximately normal population of heights of male college students with mean ì = 69 inches and standard deviation of ó = 4.6 inches. A random sample of 25 heights is obtained.
(b) Find the proportion of male college students whose height is greater than 69 inches. (Give your answer correct to four decimal places.)
.8212
(e) Find P(x > 70). (Give your answer correct to four decimal places.)
0.8212 .
(f) Find P(x < 67). (Give your answer correct to four decimal places.)
.8211
Don't need to waste your time on working this, already to late.
To find the proportion of male college students whose height is greater than 69 inches (part b), you can use the standard normal distribution.
Step 1: Calculate the z-score
The z-score formula is given by:
z = (x - mean) / standard deviation
In this case, x = 69 (height), mean = 69 inches, and standard deviation = 4.6 inches.
Calculating the z-score:
z = (69 - 69) / 4.6 = 0
Step 2: Find the proportion
Using a standard normal distribution table or a calculator, you can find the proportion corresponding to the z-score of 0. In this case, the proportion is 0.5000 (50%).
However, we are interested in finding the proportion of heights greater than 69 inches. Since the distribution is symmetric, you can subtract the proportion you found from 0.5 to get the proportion of heights greater than 69 inches:
Proportion = 1 - 0.5 = 0.5000 (50%)
Therefore, the proportion of male college students whose height is greater than 69 inches is 0.5000.
To find P(x > 70) (part e), you can follow a similar process.
Step 1: Calculate the z-score
z = (x - mean) / standard deviation
In this case, x = 70 (height), mean = 69 inches, and standard deviation = 4.6 inches.
Calculating the z-score:
z = (70 - 69) / 4.6 ≈ 0.2174
Step 2: Find the proportion
Using a standard normal distribution table or a calculator, you can find the proportion corresponding to the z-score of 0.2174. The proportion is approximately 0.5832.
However, we are interested in finding the proportion of heights greater than 70 inches. Since the distribution is symmetric, you can subtract the proportion you found from 0.5 to get the proportion of heights greater than 70 inches:
Proportion = 1 - 0.5832 ≈ 0.4168
Therefore, the probability (proportion) of getting a height greater than 70 inches is approximately 0.4168.
To find P(x < 67) (part f), again follow a similar process.
Step 1: Calculate the z-score
z = (x - mean) / standard deviation
In this case, x = 67 (height), mean = 69 inches, and standard deviation = 4.6 inches.
Calculating the z-score:
z = (67 - 69) / 4.6 ≈ -0.4348
Step 2: Find the proportion
Using a standard normal distribution table or a calculator, you can find the proportion corresponding to the z-score of -0.4348. The proportion is approximately 0.3336.
Therefore, the probability (proportion) of getting a height less than 67 inches is approximately 0.3336.