One in four adults is currently on a diet. You randomly select ten adults and ask them if they are currently on a diet. Find the probability that the number who say they are currently on a diet is (a) exactly three, (b) at least three, (c) more then three, (d) at most four, and (e) less than six.

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 13 feet per year and σ = 2.2 feet per year. Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.) (a) an escape dune will move a total distance of more than 90 feet in 6 years (b) an escape dune will move a total distance of less than 80 feet in 6 years (c) an escape dune will move a total distance of between 80 and 90 feet in 6 years

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 16 feet per year and σ = 2.9 feet per year. Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.)

(a) an escape dune will move a total distance of more than 90 feet in 6 years

(b) an escape dune will move a total distance of less than 80 feet in 6 years

(c) an escape dune will move a total distance of between 80 and 90 feet in 6 years

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 14 feet per year and σ = 3.2 feet per year. Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.)

(a) an escape dune will move a total distance of more than 90 feet in 7 years

(b) an escape dune will move a total distance of less than 80 feet in 7 years

(c) an escape dune will move a total distance of between 80 and 90 feet in 7 years

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 10 feet per year and σ = 3.8 feet per year. Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.) (a) an escape dune will move a total distance of more than 90 feet in 9 years .5000 Correct: Your answer is correct. (b) an escape dune will move a total distance of less than 80 feet in 9 years .3850 Incorrect: Your answer is incorrect. (c) an escape dune will move a total distance of between 80 and 90 feet in 9 years

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 14 feet per year and σ = 3.9 feet per year.

Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.)

(a) an escape dune will move a total distance of more than 90 feet in 7 years


(b) an escape dune will move a total distance of less than 80 feet in 7 years


(c) an escape dune will move a total distance of between 80 and 90 feet in 7 years

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 10 feet per year and σ = 3.7 feet per year.

Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.)

(a) an escape dune will move a total distance of more than 90 feet in 9 years

(b) an escape dune will move a total distance of less than 80 feet in 9 years

(c) an escape dune will move a total distance of between 80 and 90 feet in 9 years

1. Suppose X has a mean 5 and standard deviation 2. Let Y= 4x-3. Determine the mean and standard deviation of Y.

2. From an urn containing 6 red and 4 white marbles, 3 are drawn with replacement. Let X be the number of red marbles selected. Define Y as the square of the number of red marbles selected. Determine E(Y) and V(Y).

3.An examiner contains 10 multiple choice questions, each with five choices. If a student guesses the answer to each question what is the probability the students exam grade is a) at least 60%, b) at least 80& c) 50% or less d) what is the students expected grade?

4.A fair pair of dice are tossed. a) determine the probability the fifth sum of seven occurs on the 15th toss. b) How many tosses of the dice are needed to obtain the fifth sum of seven and with what standard deviation.

In a study of exercise, a large group of male runners walk on a treadmill for six minutes. After this exercise, their heart rates vary with mean 8.6 beats per five seconds and standard deviation 1.1 beats per five seconds. This distribution takes only whole-number values, so it is certainly not Normal. (Round your answers to four decimal places.)

(a) Let x be the mean number of beats per five seconds after measuring heart rate for 24 five-second intervals (two minutes). What is the approximate distribution of x according to the central limit theorem?

(b) What is the approximate probability that x is less than 8?

(c) What is the approximate probability that the heart rate of a runner is less than 100 beats per minute? (Hint: Restate this event in terms of x.)

to meet the demand for water in a region it is decicded that a dam should bu built in a river.the capacity of the dam is 3 units.the probability distribution of the number of units of water that flow into the dam during each week is given by p0=1/8, p1=1/4, p2=1/2 and p3=1/8(i.e. pi=probability that i units will flow into the dam during a week).If the supply of water by the river exceeds the remaining capacity of the dam,the excess that water is lost.the demand for water is 2 units in each week where it is assumed that the water has to be provided at the beginning of each week.ıf the dam does not contain enough water to satisfy the demand,the shortage will be fulfilled at a cost of 10 per unit shortage.the weekly depreciation cost of the dam is 2.5

a)find the transition matrix of the markov chain.

b)determine the long runaverage cost per week.

hint:let the state be the number of units of water in the dam at the end of each week.