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 sanddunes, 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 dunemoves 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, dunemovement 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 thedune). Let us assume that x has a normal distribution with = 14 feet per year and a = 4.2 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.)USE SALT(a) an escape dune will move a total distance of more than 90 feet in 7 years0.8461x(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 yearsNeed Help?Read ItLet x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of the x distribution is about $44 and the estimated standard deviation is about $9.USE SALT(a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent bythese customers due to impulse buying? What are the mean and standard deviation of the x distribution?The sampling distribution of x is approximately normal with meanO The sampling distribution of is approximately normal with meanThe sampling distribution of is not normal.O The sampling distribution of x is approximately normal with mean = 44 and standard error = $0.23.= 44 and standard error = $1.42.= 44 and standard error d= $9.Is it necessary to make any assumption about the x distribution? Explain your answer.O It is necessary to assume that x has approximately normal distribution.O It is not necessary to make any assumption about the x distribution because is large.It is not necessary to make any assumption about the x distribution because n is large.O It is necessary to assume that has a large distribution.(b) What is the probability that is between $41 and $47? (Round your answer to four decimal places.)(c) Let us assume that has a distribution that is approximately normal. What is the probability that is between $41 and $47? (Round your answer to four decimal places.)

Question

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 sanddunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the &#34;escaping&#34; dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dunemoves in and takes over. Such dunes are called &#34;escape dunes&#34; 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, dunemovement 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 thedune). Let us assume that x has a normal distribution with = 14 feet per year and a = 4.2 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.)USE SALT(a) an escape dune will move a total distance of more than 90 feet in 7 years0.8461x(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 yearsNeed Help?Read ItLet x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of the x distribution is about $44 and the estimated standard deviation is about $9.USE SALT(a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent bythese customers due to impulse buying? What are the mean and standard deviation of the x distribution?The sampling distribution of x is approximately normal with meanO The sampling distribution of is approximately normal with meanThe sampling distribution of is not normal.O The sampling distribution of x is approximately normal with mean = 44 and standard error = $0.23.= 44 and standard error = $1.42.= 44 and standard error d= $9.Is it necessary to make any assumption about the x distribution? Explain your answer.O It is necessary to assume that x has approximately normal distribution.O It is not necessary to make any assumption about the x distribution because is large.It is not necessary to make any assumption about the x distribution because n is large.O It is necessary to assume that has a large distribution.(b) What is the probability that is between $41 and $47? (Round your answer to four decimal places.)(c) Let us assume that has a distribution that is approximately normal. What is the probability that is between $41 and $47? (Round your answer to four decimal places.)

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