Statistics and Probability Answers

A parabolic satellite dish reflects signals to the dish’s focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function

𝑓𝑥(𝑥) = {𝑐 (1 −(1/16) 𝑥*2 , 0 < 𝑥 < 2

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒}

where X is the distance (in meters) from the centroid of the dish surface to a reflection point at which a signal arrives. Determine the following: a. Value of 𝑐 that makes 𝑓𝑥(𝑥) a valid probability density function.

b. 𝑃(0.1 < 𝑋 < 0.4).

c. 𝐸(𝑋) and 𝑉𝑎𝑟(X)

Researchers wish to test the effectiveness of a certain drug in lowering the cholesterol levels in individuals aged 50-60 years old. The mean cholesterol levels in previous researches for this age group is 250 mg/dL. The normal range is 200-239 mg/dL. 50 participants were invited to the study, The mean cholesterol levels for the participants after a month of taking the medication is 237 mg/dL with a standard deviation of 4 mg/dL. Assuming a normal distribution of times of labor, test at the 10% level of significance test whether the mean cholesterol level is less than 250 mg/dL.

Question #333210

. ACTIVITY 1. Use the ANOVA to show if there is significant difference among the sales of the three candidates for promotion.

Sales of three candidates for promotion.

A B C

12450 16500 12800

12100 13300 16500

11200 11400 18000

15000 12500 11900

13000 14600 28300

15400 14580 12200

11400 11200 19000

15100 15300 19000

15600 18000 55000

∑𝐴 = ∑𝐴² =

∑𝐵 = ∑𝐵² =

∑𝐶 = ∑

3. According to the report of National Economic Development Authority (NEDA) last year, a Filipino household spends an average of 1333 a day. You took a random sample of 20 households and determined the amount of their allotted budget each day revealing a mean of P420 and standard deviation of P120. Using 0.01 level of significance, can it be concluded that the average amount spent per day by a Filipino household has increased? Assume normality over the population.

Estimate kurtosis.

XFrequency

1 – 512

5 – 1011

10 – 1510

15 – 204

20 – 253