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.)
(e) Find P(x > 70). (Give your answer correct to four decimal places.) 0.1587 was my answer .
(f) Find P(x < 67). (Give your answer correct to four decimal places.) 0.0228
was my answer .
b) mean = median = mode. See definition of median.
e) Z = (score-mean)/SD for raw scores. Answer wrong.
Z = (score-mean)/SEm for means. Answer wrong.
SEm = SD/√n = 4.6/√25 = 4.6/5 = .92
f) Use same process.
Use Table indicated in later post.
I understand the median is when you arrange the numbers from small to large and it is the middle number. If I write down 1-69, middle number is 35 but the answer ask for it in four decimal places and that answer is wrong and (e) and (f). e I came up with 0.001 and (f) I am not really sure of.
To find the proportion of male college students whose height is greater than 69 inches, we need to use the standard normal distribution.
(b) Calculating the proportion:
1. Convert the given value of 69 inches to a z-score. The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation.
In this case, x = 69 inches, μ = 69 inches, and σ = 4.6 inches.
Plugging in the values, we get:
z = (69 - 69) / 4.6 = 0
2. Look up the z-score in the standard normal distribution table (also known as the Z-table) to find the corresponding proportion.
The proportion corresponding to a z-score of 0 is 0.5000.
However, we need to find the proportion whose height is greater than 69 inches, not equal to 69 inches. Since the standard normal distribution is symmetrical, we can subtract 0.5000 from 1 to get the desired proportion:
Proportion = 1 - 0.5000 = 0.5000
So, the proportion of male college students whose height is greater than 69 inches is 0.5000.
(e) To find P(x > 70), we repeat the same steps as above.
1. Convert the value of 70 inches to a z-score:
z = (70 - 69) / 4.6 = 0.2174 (rounded to four decimal places)
2. Look up the z-score in the standard normal distribution table to find the corresponding proportion.
From the z-table, we find that the proportion corresponding to a z-score of 0.2174 is 0.5868.
However, we need to find P(x > 70), which means finding the proportion greater than 70 inches. Since the standard normal distribution is symmetrical, we subtract the obtained proportion from 1 to get the desired proportion:
Proportion = 1 - 0.5868 = 0.4132
So, P(x > 70) is approximately 0.4132.
(f) To find P(x < 67), we again repeat the same steps.
1. Convert the value of 67 inches to a z-score:
z = (67 - 69) / 4.6 = -0.4348 (rounded to four decimal places)
2. Look up the z-score in the standard normal distribution table to find the corresponding proportion.
From the z-table, we find that the proportion corresponding to a z-score of -0.4348 is 0.3325.
So, P(x < 67) is approximately 0.3325.