Question

SnoopPro is a global company specializing in communications security. The company monitors over 1 billion Internet messages per day and recently reported that 70% of emails are spam. Suppose your inbox contains 25 messages. Let X be the number of messages that are spam. What is P(16 ≤ X ≤ 20)?

If a sample of size n = 64 is selected from a population with mean E(X) = 50 and standard deviation SD(X) = 8, then the probability that the sample mean x is less than 52 is:

The Central Limit Theorem states that

The distribution of the population mean μ will be about normal provided that the sample size n is sufficiently large

The sampling distribution of the sample proportion p̂ will be approximately normal provided that the population is normally distributed    

The sampling distribution of the sample mean x will be about normal provided that the sample size n is sufficiently large

The sample mean x will always equal the population mean μ when the sample size n is large enough.

As the sample size n gets larger and larger, the sampling distribution of the sample mean x is less concentrated around the central value

If the sample size n is large, then z follows a standard normal distribution, provided that the population is normally distributed

A sample of size n = 36 is selected from a population with mean E(X) = 55 and standard deviation SD(X) = 27. The expected value E(x) and standard deviation SD(x) of the sampling distribution of the sample mean x are:

The two curves below represent the sampling distribution of the sample mean X for two different sample sizes: n = 256 and n = 576.

In both cases the samples are selected from the same population.

Note that the standard deviation for sampling distribution A is SD(X) = 8 and for sampling distribution B the standard deviation is SD(X) = 12.

Question 1. Sampling distribution B comes from the sample that had sample size n =

Question 2. What is the standard deviation SD(X) of the population from which the samples are taken?

Answer 1

(1)

Question:

SnoopPro is a global company specializing in communications security. The company monitors over 1 billion Internet messages per day and recently reported that 70% of emails are spam. Suppose your inbox contains 25 messages. Let X be the number of messages that are spam. What is P(16 ≤ X ≤ 20)?

n = 25

p = 0.70

q = 1 - p = 0.30

= np = 25 X 0.70 = 17.5

To find P(16 ≤ X ≤ 20):

Applying Continuity Correction:

P(15,5 < X < 20.5):

For X = 15.5:

Z = (15.5 - 17.5)/2.2913

= - 0.8729

By Technology, cumulative area under standard normal curve = 0.1914

For X = 20.5:

Z = (20.5 - 17.5)/2.2913

= 1.3093

By Technology, cumulative area under standard normal curve = 0.9048

So,

P(16 ≤ X ≤ 20) = 0.9048 - 0.1914 = 0.7134

Do,

Answer is:

0.7134

(2)

Question:

If a sample of size n = 64 is selected from a population with mean E(X) = 50 and standard deviation SD(X) = 8, then the probability that the sample mean x is less than 52 is:

= 50

= 8

n = 64

SE = /

= 8/

= 1.00

To find P(<52):

Z =(52 - 50)/1.00

= 2.00

By Technology, cumulative area under standard normal curve = 0.9772

So,

P(<52):= 0.9772

So,

Answer is:

0.9772

(3)

Question:

The Central Limit Theorem states that

Correct option:

The sampling distribution of the sample mean will be about normal provided that the sample size n is sufficiently large

(4)

Question:

A sample of size n = 36 is selected from a population with mean E(X) = 55 and standard deviation SD(X) = 27. The expected value E(x) and standard deviation SD(x) of the sampling distribution of the sample mean are:

(i)

The expected value E(x) of the sampling distribution of the sample mean is = Population Mean = 55

(ii)

The standard deviation SD(x) of the sampling distribution of the sample mean is =

AS PER DIRECTIONS FOR ANSWERING, FIRST 4 QUESTIONS ARE ANSWERED.