e percent of fat calories that a person in America consumes each day is consistently appropriated with a mean of around 36 and a standard deviation of 10. Expect that one individual is subjectively picked. Let X=X= percent of fat calories.

(a) Find the z-score identifying with 41% of fat calories, acclimated to 3 decimal spots.

(b) Find the probability that the percent of fat calories an individual consumes is more than 41.

(c) Shade the area identifying with this probability in the chart underneath. (Hint: The x-turn is the z-score. Use your z-score from segment (a), changed in accordance with one decimal spot).

(d) Find the most limit number for the lower quarter of percent of fat calories. Round your reaction to 3 decimal spots.

(e) Sketch the graph and form the probability announcement.

A typical of 1 group is transported off a laborer in 1 second. The laborer, on the other hand, uses the 5 packages that come to it.

is setting up a document. The time between groups is exhibited as an extraordinary unpredictable variable. X of the laborer

Let it be an unpredictable variable imparting the time it takes to set up a report. Passing for the status of a document

your time

a. Find the probability that it is more than 10 seconds.

b. Find the probability that it is between 5 seconds and 10 seconds.

Expect that the length of a particular sort of criminal primer is known to be ordinarily scattered with a mean of 21 days and a standard deviation of seven days.

(a) In words, describe the subjective variable X.

(b) Find the z-score for a primer suffering 18 days. (Round your reaction to three decimal spots.)

(c) If one of the primers is erratically picked, find the probability that it suffered at any rate 18 days.

(d) Shade the district identifying with this probability in the graph underneath. (Hint: The x-center is the z-score. Use your z-score from part (b), acclimated to one decimal spot).

(e) 58% of all primers of this sort are done inside how long?

Accept that the distance of fly balls hit to the outfield (in baseball) is consistently passed on with a mean of 260 feet and a standard deviation of 51 feet.

Use your outlining calculator to react to the going with requests. Make your answers in percent structure. Round your reactions to the nearest tenth of a percent.

a) If one fly ball is erratically perused this transport, what is the probability that this ball journeyed under 192 feet?

PP(fewer than 192 feet) = %

b) If one fly ball is indiscriminately perused this apportionment, what is the probability that this ball journeyed more than 234 feet?

PP(more than 234 feet) = %

The statistics Association of XYZ University would like to determine whether there is a relationship between student interest in statistics and ability in Mathematics. A random sample of 400 students is selected and they are asked whether their ability in mathematics and interest statistics are low, average, or high. The results were as follows: Interest in Ability in Mathematics Statistics Low Average High Total Low 80 45 40 165 . Average 35 65 30 130 High 25 30 50 105 Total 140 140 120 400 At the 0.01 significance level, is there a relationship between interest in statistics and ability in mathematics?College of Arts & Sciences Department of Mathematics, Statistics & Physics Mathematics Program Mathematics for Engineers (MATH 217) Instructor : Or Mahmoud BOUTEFNOUCHET QUIZ 4 Question: 1. Write the following homogeneous system of differential equation: x'(t) = y(t) +z(t) (') y' (t) = x(t) + z(t) z'(t ) = x(t) + y(t) in the matrix form X'(1) = A . X(t) 2. Find the eigenvalues and the eigenvectors of the matrix A 3. Find the general solution of the system (")1 pts Question 17 The Starfleet Academy currently has 400 business students. Of these 400 students, 188 are currently enrolled in accounting and 132 are 1 currently enrolled in business statistics. It is also known that 30 business students are currently enrolled in both courses. One business student is randomly selected, It/What is the probability that the student was enrolled in Business Statistics but was not enrolled in Accounting? Previous1. Suppose that at Point Park University, NSET Department, the following describes registrations in three courses: 240 students altogether have taken the following classes: 60 took Mathematical Statistics, call "Mathematical Statistics" event MS 100 took Calculus II, call "Calculus II" event CII 80 took Calculus III, call "Calculus III" event CIII 20 students took Mathematical Statistics and Calculus II 15 Students took Mathematical Statistics and Calculus III 10 Students took Calculus II and Calculus III. 5 students took all three classes. a) Produce a diagram with 3 overlapping circles and fill in all numbers. b) find the probability of events: p(MS U CII U CIII) **must show how you found such probability