Question

1. Suppose that a survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax. Suppose that 40% of all adults in Ohio support the increase. We independently select 7 adults at random and record their status in supporting the increase. What is the probability that exactly 4 people support the increase in tax?

Group of answer choices

0.2419

0.5162

0.1935

0.4838

2. A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of ?⎯⎯\overline{x} is

Group of answer choices

approximately normal because of the central limit theorem.

approximately normal because ?⎯⎯\overline{x} is always approximately normally distributed.

normal if the population is normally distributed.

approximately normal because the sample size is large in comparison to the population size.

3. The standard deviation of a normal distribution

is always 0.

is always 1.

cannot be negative.

can be any value.

4.

Out of a group of 6 students, you want to create a team of 4 people. How many different teams of students can we make?

Group of answer choices

120

24

360

15

5.

The probability that X is between 1.5 and 2.5 is:

Group of answer choices

1/2

1/4

3/4

0

Answer 1

1)

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.4

N = number of trials = 7

R = desired success = 4

P(4) = 7c4*(0.4^4)*(1-0.4)^7-4 = 0.1935