A sample of size 100 is selected from a population with p = .40. a. What is the expected value of p(bar)?
b. What is the standard error of p(bar)?
c. Show the sampling distribution of p(bar)?
d. What does the sampling distribution of p show?

(a) 0.40

(b) 0.049

(c)

(d) Explained below

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

The standard deviation of this sampling distribution of sample proportion is:

Given:

n = 100

p = 0.40

As n = 100 > 30 the Central limit theorem is applicable.

(a)

Compute the expected value of as follows:

The expected value of is 0.40.

(b)

Compute the standard error of as follows:

The standard error of is 0.049.

(c)

The sampling distribution of is:

(d)

The sampling distribution of p show that as the sample size is increasing the distribution is approximated by the normal distribution.

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m