Question

A retail carpet business has primarily residential customers together with a few commercial customers that make large purchases. Usually, the business sells an average of 100 square yards of carpet with a standard deviation of 90 square yards. The distribution of carpet sales is

Select one:

a. right-skewed.

b. left-skewed.

c. skewed, but we can’t tell whether it’s left-skewed or right-skewed

d. approximately symmetric, but not Normal.

e. approximately Normal.

f. There’s no way to tell what shape the distribution has.

g. It doesn't make sense to talk about the shape of this distribution.

Suppose the histogram in FIGURE 3 is the sampling distribution for sample averages from samples of size n = 25 from some population. Which of the following statements would be true if the sample sizes were increased to 150?

Select one:

a. The shape of the distribution would not change.

b. The shape of the distribution would be more bell-shaped.

c. The shape of the distribution would be more skewed.

"95% confident" means...

Select one:

a. if we took many random samples from the population, and computed a 95% confidence interval for each sample, we would expect 95% of the confidence intervals to contain the true parameter.

b. if we took one random sample from the population, we would expect 95% of the people in the sample to have a value within the confidence interval.

c. Both A and B are true

d. Neither A nor B are true

Using the sampling distribution in FIGURE 3, how likely is a sample mean around 76?

Select one:

a. Reasonably likely to occur from a sample of this size

b. Unusual but might occur occasionally

c. Extremely unlikely to ever occur

We have a large collection (5574) of real SMS text messages from cellphone users in 2010. 747 of these messages are classified as "spam", and the rest are not. The word “text” (or “txt”) is contained in 7.01% of legitimate (not spam) messages, and in 38.55% of all spam messages. What is the probability that a message is spam, given that it contains the word “text” (or “txt”)?

Select one:

a. 7.01%

b. 13.40%

c. 38.55%

d. 45.97%

e. 57.56%

f. 84.61%

g. We can't determine this probability.

Answer 1

• Residential customers are more that means frequency is high but size of carpet is small compared to commercial purchase. There are few commercial customers that make large purchases. So it will be right-skewed ( option a)
• We know from central limit theorem, if sample size increases and if it is greater than 30 then the sample mean follows approximately normal. Here initial sample size was 25, present sample size isis 150. So, the shape of the distribution would be more bell shaped (option b)
• From definition of confidence interval we know 95% confident" means

  95% confident" means if we took many random samples from the population, and computed a 95% confidence interval for each sample, we would expect 95% of the confidence intervals to contain the true parameter.(option a is correct)

• To solve this figure 3 is required, which is missing.

• Probability that a sms is spam = 747/5574=0.134.

So, probability that it is not spam is 1-0.134=0.866. P("text" |spam) =0. 3855

P("text"|not spam) =0.0701

Probaility of getting the word "text" = P("text")

=P("text" | spam) *P(spam) +P("text| not spam) *P(not spam)

=. 3855*0.134+. 0701*.866=.11236

P(spam|"text")=P( "text" | spam) *P (spam) / P("text")

=0. 3855*0.134/.11236

=0.4597

Correct answer is option d)

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