According to TMUSS Quarterly (Totally Made-Up Sports Statistics) April 2017, the probability that the Tampa Bay Buccaneers will

Answer:

(a) P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) P(X ≥ 13.01) = 0.3075

Step-by-step explanation:

To address this problem, one needs to grasp the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems involving normally distributed samples are resolved through the application of the z-score formula.

In a data set with a mean and standard deviation , the z-score for a measurement X is defined as:

The Z-score indicates how many standard deviations the measurement deviates from the mean. After determining the Z-score, one can consult the z-score table to find the relevant p-value for that score. This p-value represents the probability that the measure's value is less than X, which indicates the percentile of X. By subtracting this p-value from 1, we obtain the likelihood that the measure's value exceeds X.

Central Limit Theorem

According to the Central Limit Theorem, for a normally distributed random variable X with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated by a normal distribution, characterized by mean and standard deviation .

The Central Limit Theorem can also be applicable to a skewed variable, provided that n is 30 or more.

In this case, we are given that:

(a) Compute P(12.99 ≤ X ≤ 13.01) when n = 16.

In this scenario, we find

This probability equates to the p-value of Z at X = 13.01 minus the p-value of Z at X = 12.99.

X = 13.01

According to the Central Limit Theorem

yields a p-value of 0.3075

0.6915 - 0.3075 = 0.3840

P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) What is the probability that the sample mean diameter is greater than 13.01 when n = 25?

P(X ≥ 13.01) =

This is obtained by subtracting the p-value of Z when X = 13.01 from 1. Hence

has a p-value of 0.6915

1 - 0.6915 = 0.3075

P(X ≥ 13.01) = 0.3075

Answer:

Using a scale of 2" means "will take the original and enlarge it to twice its size".

Thus, the resulting photocopy will be double the dimensions of the original.

Step-by-step explanation:

Answer:

________{0.50 if x < 3

________{1.00 if 3 ≤ x < 6

f(x) = ____{1.50 if 6 ≤ x < 9

________{2.00 if 9 ≤ x < 12

Step-by-step explanation:

Based on the details provided:

Employees with less than 3 years receive an increase of $0.50 hourly

Employees with at least 3 years but under 6 years receive $1.00 increase hourly

Employees with a minimum of 6 years and less than 9 get $1.50 increase hourly

Employees with at least 9 years but below 12 years receive $2.00 increase hourly

This information can be expressed as a piecewise function:

________{0.50 if x < 3

________{1.00 if 3 ≤ x < 6

f(x) = ____{1.50 if 6 ≤ x < 9

________{2.00 if 9 ≤ x < 12

The conditions are outlined in the piecewise function above with x indicating the number of years employed.

Response:

Detailed explanation:

a) this situation has a two-tailed test

The critical value is found using the t distribution table.

α = 1 - 0.95 = 0.05

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Consulting 0.975 with df 10

The critical value obtained is 2.228

b) α = 1 - 0.95 = 0.05

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Consulting 0.975 with df 20

The critical value obtained is 2.086

c) α = 1 - 0.99 = 0.01

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

Consulting 0.995 with df 20

The critical value obtained is 2.845

d) α = 1 - 0.99 = 0.01

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

Consulting 0.995 with df 60

The critical value obtained is 2.660

e) 1 - α = 1 - 0.01 = 0.99

Consulting 0.99 with df 10

The critical value obtained is 2.764

f) 1 - α = 1 - 0.025 = 0.975

Consulting 0.975 with df 5

The critical value obtained is 2.571