1} Assuming that the heights of college women are normally distributed with mean69inches and standard deviation3.3inches, answer the following questions. (Hint: Use the figure below with meanand standard deviation.)(a) What percentage of women are taller than69inches? % (b) What percentage of women are shorter than69inches? % (c) What percentage of women are between65.7inches and72.3inches? % (d) What percentage of women are between62.4and75.6inches? %

2) The incubation time for a breed of chicks is normally distributed with a mean of28days and standard deviation of approximately3days. Look at the figure below and answer the following questions. If1000eggs are being incubated, how many chicks do we expect will hatch in the following time periods? (Note: In this problem, let us agree to think of a single day or a succession of days as a continuous interval of time. Assume all eggs eventually hatch.)(a) in22to34days chicks (b) in25to31days chicks (c) in28days or fewer chicks (d) in19to37days chicks

3) It's truesand 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? Letxbe a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume thatxhas a normal distribution with=11feet per year and=2.2feet 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 in7years (b) an escape dune will move a total distance of less than 80 feet in7years (c) an escape dune will move a total distance of between 80 and 90 feet in7years

4) (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 by these 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 mean _x = 44 and standard error _x = $0.23.The sampling distribution of x is approximately normal with mean _x = 44 and standard error _x = $1.42. The sampling distribution of x is approximately normal with mean _x = 44 and standard error _x = $9.The sampling distribution of x is not normal. Is it necessary to make any assumption about the x distribution? Explain your answer. It is not necessary to make any assumption about the x distribution because n is large. It is necessary to assume that x has a large distribution. It is necessary to assume that x has an approximately normal distribution. It is not necessary to make any assumption about the x distribution because is large.(b)What is the probability that x is between $41 and $47? (Round your answer to four decimal places.)(c)Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $41 and $47? (Round your answer to four decimal places.)(d)In part (b), we used x, the average amount spent, computed for 40 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen? The x distribution is approximately normal while the x distribution is not normal. The standard deviation is smaller for the x distribution than it is for the x distribution. The standard deviation is larger for the x distribution than it is for the x distribution. The mean is larger for the x distribution than it is for the x distribution. The sample size is smaller for the x distribution than it is for the x distribution. In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer? The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer. The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.