Question 1146208: Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a men of 183 cm and standard deviation of 10.5cm.
A.What is the probability that a Dutch male is shorter than 175 cm?
B.What is the probability that a Dutch male is taller than 195 cm?
C.What is the probability that a Dutch male is between 173 and 193 cm?
D. Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! A.What is the probability that a Dutch male is shorter than 175 cm?
 =  = -0.76
Look up -0.76 on a z-table, and you get a result of 0.2266. This means there is a 0.2266 probability a Dutch male is shorter than 175 cm.
B.What is the probability that a Dutch male is taller than 195 cm?
 =  = 1.14
Look up 1.14 on a z-table, and you get a result of 0.8729. This means there is a 0.8729 probability a Dutch male is SHORTER than 195 cm. However, the questions asks what the probability is that a Dutch male is TALLER than 195 cm. To find this, simply subtract the result of 0.8729 from 1 to get an answer of 0.1271.
C.What is the probability that a Dutch male is between 173 and 193 cm?
First, find the probability a that Dutch male is shorter than 193 cm.
 =  = 0.95
Look up 0.95 on a z-table, and you get a result of 0.8289. This means there is a 0.8289 probability a Dutch male is shorter than 193 cm.
Second, find the probability that a Dutch male is shorter than 173 cm.
 =  = -0.95
Look up -0.95 on a z-table, and you get a result of 0.1711. This means there is a 0.1711 probability a Dutch male is shorter than 173 cm.
To find what the probability is that a Dutch male is between 173 cm and 193 cm, simply subtract the second result (0.1711) from the first result (0.8289) to get an answer of 0.6578.
D. Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?
First, find the probability a Dutch male is taller than 190 cm.
 =  = 0.67
Look up 0.67 on a z-table, and you get a result of 0.7486. This means there is a 0.7486 probability a Dutch male is SHORTER than 190 cm. However, we want to know what the probability is that a Dutch male is TALLER than 190 cm. To find this, simply subtract the result of 0.7486 from 1 to get an answer of 0.2514. This means 25.14% of Dutch men are taller than 190 cm.
Back to the original question. Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?
1000 * 0.2514 = 251.4
To round off to a whole number, out of a random sample of 1000 Dutch men, we would expect 251 of them to be taller than 190 cm.
|
|
|
