Kindly help me solve all of the following problems please

A dignitary of a business college needs to know whether the extent of graduates who utilize measurable induction inside the primary year after graduation is more noteworthy than 0.6. Assume the test measurement was discovered to be 3.92. At the = 0.10 degree of importance, what might be the end?

Answer utilizing just the data introduced in this inquiry; don't allude to your responses to whatever other inquiries that may have a comparable set-up.

Peruse cautiously, and select all that apply!

Can't reason that the genuine mean number of graduates who utilize factual deduction one year after graduation is more prominent than 0.60. That is, the Dean can't guarantee that a normal of in excess of 60 alumni utilize measurable induction one year after graduation.

Can't reason that the genuine extent of graduates who utilize factual surmising one year after graduation is more noteworthy than 0.60. That is, the Dean can't guarantee that over 60% of graduates utilize factual deduction one year after graduation.

Reason that the genuine extent of graduates who utilize measurable induction one year after graduation is more prominent than 0.60. That is, over 60% of graduates utilize measurable surmising one year after graduation.

Reason that the genuine mean number of graduates who utilize measurable deduction one year after graduation is more prominent than 0.60. That is, a normal of 60 alumni utilize measurable induction one year after graduation.

Reject the elective theory

Presume that the genuine mean number of graduates who utilize factual induction one year after graduation is more prominent than 60/300 = 0.20. That is, over 20% of graduates utilize measurable surmising one year after graduation.

Reject the invalid speculation.

Presume that the genuine extent of graduates who utilize measurable deduction one year after graduation is more prominent than 0.10. That is, over 10% of graduates utilize factual derivation one year after graduation.

Neglect to dismiss the invalid theory

2. The Normal Distribution The standard normal (or Gaussian) distribution is frequently used in statistics. This is the "bell curve" ex- /2 given by the graph of 4(x) = V2TT . A fundamental property of probability distributions is that the total area under the graph is 1. We will use multivariable calculus to verify this for the normal distribution. (a) For a > 0 sketch the quarter disks Di = {(x, y) : x2 +y? N(D,I'l(9]) for every E B. Let X], . . . ,Xn be i.i.d. observations from repeated trials ofthe experiment. Let II N;- = 2 10f.- = :0 i=1 he the counts of the number each outcome is observed in the data. In probability theory, the Normal Distribution (sometimes called a Gaussian Distribution or Bell Curve) is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Describing the normal distribution using a mathematical function is called a probability distribution function (PDF) which is given here: 1 (x-1) 2 Normal Distribution Function f (x) =- # = The mean of the distribution e 202 ov2n = The standard deviation We can find the probability that a randomly selected data point x will fall in the range a S x S B by the integrating the normal PDF from a to B. i.e. P(a S x SB) = SF f(x)dx. Here is the problem you will solve: The lengths of a certain population of Atlantic croaker fish are normally distributed with average length of #4 = 10 inches and standard deviation o = 2. Find the probability that a randomly selected croaker from this population will be between a = 11 inches and B = 13 inches. . 25 Note: The normal distribution function is 4 . 20 essentially f(x) = e"*which is a non-integrable +.15 function. This means we can use its MacLaurin series expansion in order to integrate. Part of solving the problem is finding out how many terms of the series you will need to get an accurate 13 result (within 0.1%).Design a computer program that generates Exponentially distributed random numbers. You can implement this using the call to a Gaussian random number generator ( Matlab function rand () ) producing a vector of random numbers of unit variance, VA. Imagine this vector as a random noise voltage signal at the input of a radar receiver. Exponential statistics are produced at the output of an envelope detector, Pn = V.^2; % noise power a. Plot a sequence of N=1000 normal distributed samples (voltage signal V.) and indicate the mean value and the standard deviations (as horizontal lines). b. Plot a histogram using the samples generated in Part a. Use an appropriated bin width to adequately describe the distribution (Le to get a reasonably smooth curve). If you use the command [n, x]=hist (Vn, nbin) , and divide the resulting number of elements in each container, n, by the product N* [x(1)-x(2)], the histogram will approximate the probability density function (PDF). Superimpose the data with the theoretical Normal distribution function calculated with the standard deviation computed in part a. c. Plot the sequence of samples for the power signal, P, and indicate the mean and standard deviation. These are exponentially distributed. d. Plot a histogram of exponentially distributed samples as in Part b