COB191 Final (problems)

If P(buy warranty)=0.18

what is P(not buy)?

What are mutually exclusive events?

Events that cannot occur together such as "product sold" and "product returned before purchase"

What are independent events?

Events that do not affect each other such as sales in two different cities

What is a contingency table used for?

To compute probabilities of joint and conditional events such as P(buys soda AND pizza)

What is conditional probability?

Probability of A given B occurred such as P(buys drink | buys fries)

If P(A)=0.30 and P(B)=0.20 and events are independent

what is P(A and B)?

If P(A)=0.25 and P(B)=0.40 and mutually exclusive

what is P(A or B)?

What is classical probability?

Probability based on known equal outcomes such as drawing a card

What is empirical probability?

Probability based on observed data such as percent of customers returning items

What does "collectively exhaustive" mean?

Events cover all possibilities such as all drink choices (water

What is the complement rule?

P(not A)=1−P(A) because total probability equals 1

If P(return)=0.12

what is P(no return)?

When do we use the binomial distribution?

When there are fixed trials

A salesman closes 40% of deals. What is P(exactly 3 closes out of 5)?

0.2304 because C(5

What is the mean of a binomial distribution?

np because average success = trials*probability

If n=50 and p=0.10 what is mean?

5 because np=50*0.1

When do we use the Poisson distribution?

When counting events over time such as number of customers per hour

If average calls = 6 per hour

what is P( exactly 2 )?

What is expected value in business terms?

Long-run average outcome such as average profit per sale over time

If average returns/day=3

what is expected value?

If λ=4 what is P(X=0)?

e⁻⁴ ≈ 0.0183 because 4⁰/0! =1

What is a z-score?

Number of standard deviations a value is from the mean: (x−μ)/σ

If μ=10 and σ=2

find z for x=14.

If deliveries are N(μ=12

σ=3) what is P(X>15)?

Why is P(X=value)=0 for continuous distributions?

One exact point has no area under the curve because probability = area

What is total area under a normal PDF?

1 because probabilities sum to 1

Which Excel function finds normal probability?

=NORM.S.DIST(z

Which Excel function finds z-critical?

=NORM.S.INV(probability)

When is data considered approximately normal?

If histogram is bell-shaped and symmetric without extreme skew

What is the empirical rule?

68% within 1σ

What is a sampling distribution?

Distribution of a statistic like x̄ from repeated samples

What does the CLT state?

For large n

What is standard error?

Standard deviation of sample means: σ/√n

If σ=30 and n=25 what is SE?

6 because SE=30/√25 = 30/5 = 6

Why does SE decrease as n increases?

Bigger samples give more accuracy so less spread in sample means

When can we assume normality of x̄?

If population is normal OR sample size n≥30 because CLT applies

What is a point estimate of μ?

The sample mean because it best estimates the population mean

What is a confidence interval?

A range of values used to estimate a population parameter

When do we use z for CI?

When σ is known or n≥30 because distribution is stable

When do we use t for CI?

When σ is unknown and sample is small

If x̄=50

σ=10

What happens to CI when confidence increases?

Interval becomes wider because more certainty requires more range

What happens when sample size increases?

CI becomes narrower because we estimate more precisely

What does “95% confident” mean?

If we repeated sampling many times

What Excel finds t-critical?

=T.INV.2T(alpha

What Excel finds z-critical?

=NORM.S.INV(1−alpha/2)

What is the null hypothesis (H₀)?

Statement of no change including equality such as μ=8

What is the alternative hypothesis (H₁)?

Statement we try to support excluding equality such as μ

What is Type I error?

Rejecting a true null such as saying average cost < $8 when it is actually ≥ $8

What is Type II error?

Failing to reject a false null such as missing that average cost is < $8

When do we reject H₀ in a right-tailed test?

If test statistic > critical value or p<alpha

When do we reject H₀ in a left-tailed test?

If test statistic < critical value or p<alpha

What does “statistically significant” mean?

Evidence strong enough to reject H₀ at chosen alpha