Question

1. Suppose we perform a binomial experiment 50 times where the probability of success on any given trial is 0.20. Which of the following is correct?

1. μ = 10 and σ = 3.16

2. μ = 8 and σ = 3.16

3. μ = 10 and σ = 2.83

4. μ = 8 and σ = 2.83

2. Suppose the average number of Funko Pops owned by a Statistics instructor is 7 with a standard deviation of 2.3 Pops. What would be the z-score of Mr. James, who owns 13 Pops?

1. z = 13

2. z = 2.61

3. z = -2.61

4. z = 1.53

3. All of the following can be approximated using a normal distribution EXCEPT

1. The number of successful outcomes for a binomial experiment with 10 trails where the probability of success on any given trail is 0.85

2. The average sample mean for samples of size 20 from a population that is normally distributed

3. The average sample mean for samples of size 50 from a population that is strongly skewed to the left

4. The number of successful outcomes for a binomial experiment with 30 trails where the probability of success on any given trail is 0.25

Answer 1

Solution:

Given that,

1.

P = 0.20

1 - P = 1 - 0.20 = 0.80

n = 50

Mean = = n*P = 50*0.20 = 10

Standard deviation = =n*p*(1-p)= 50*0.20*0.80 = 8 = 2.83

Option c is correct.

2.

Solution :

Given that,

mean = = 7

standard deviation = = 2.3

X = 13

z= (X - ) /

= (13 - 7 ) / 2.3

= 2.61

Option b. is correct.

3.

P = 0.25

1 - P = 0.75

n = 30

Here, BIN ( n , P ) that is , BIN (30 , 0.25)

then,

n*p = 30*0.25 = 7.5 > 5

n(1- P) = 30*0.75 = 22.5 > 5

Option d is correct.

Option d can be approximated using a normal distribution.