Question

​You'd like to estimate the proportion of the 12,152 full-time undergraduate students at a university who are foreign students. You poll a random sample of 50 ​students, of whom 7 are from foreign countries. Unknown to ​you, the proportion of all undergraduate students who are foreign students is 0.06.
Let X denote a random variable for which x=1 denotes foreign students and x=0 denotes students from the U.S. Complete parts​ (a) through​ (c).

a. Describe the data distribution.

The data distribution consists of ( )​1's (denoting a foreign ​student) and ( )0's (denoting a student from the​ U.S.).

b. Describe the population distribution.

The population distribution consists of the​ x-values of the population of 12,152 full-time undergraduate students at the​university, ( )​% of which are​ 1's (denoting a foreign​ student) and ( )% of which are​ 0's (denoting a student from the​ U.S.).

c. Find the mean and standard deviation of the sampling distribution of the sample proportion for a sample of size 50.

The mean is ( )

The standard deviation is ( )​(Round to four decimal places as​needed.)

Explain what this sampling distribution represents.

The sampling distribution represents the probability distribution of the ( ) proportion of foreign students in a random sample of ( )students. In this​case, the sampling distribution is approximately normal with a mean of ( ) and a standard deviation of ( )

Answer 1

Answer:

a) The data distribution consists of ( 7 )​1's (denoting a foreign ​student) and ( 43 )0's (denoting a student from the​ U.S.).

b) The population distribution consists of the​ x-values of the population of 12,152 full-time undergraduate students at the​university, ( 6 )​% of which are​ 1's (denoting a foreign​ student) and ( 94 )% of which are​ 0's (denoting a student from the​ U.S.).

c) The mean is ( 0.06 )

The standard deviation is ( 0.0336 )

The sampling distribution represents the probability distribution of the ( sample ) proportion of foreign students in a random sample of ( 50 ) students. In this​ case, the sampling distribution is approximately normal with a mean of ( 0.06 ) and a standard deviation of ( 0.0336 )

Step-by-step explanation: