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Normal distributions

### Consider two independent populations that are normally distributions. A simple random sample of $$\displaystyle{n}_{{1}}={41}$$ from the first population showed $$\displaystyle\overline{{x}}_{{11}}={33}$$, and a simple random of size $$\displaystyle{n}_{{2}}={48}$$ from the second population showed $$\displaystyle\overline{{x}}_{{2}}={32}$$ Suppose $$\displaystyle{s}_{{1}}={9}{s}_{{1}}={9}{\quad\text{and}\quad}{s}_{{2}}={10}{s}_{{2}}={10}$$, find a 98% confidence interval for $$\displaystyle\mu_{{1}}−\mu_{{2}}\mu_{{1}}-\mu_{{2}}$$. (Round answers to two decimal places.) margin of error-? lower limit-? upper limit-?

Normal distributions

### Explain some of the important characteristics of a normal distribution.

Normal distributions

### A normal distribution has $$\mu = 30$$ and $$\sigma = 5$$. (c)Find the raw score corresponding to $$z =-2$$.

Normal distributions

### Consider the marks of all 1st-year students on a statistics test. If the marks have a normal distribution with a mean of 72 and a standard deviation of 9, then the probability that a random sample of 10 students from this group have a sample mean between 71 and 73 is?

Normal distributions

### $$\displaystyle{\left(\mu{1}-\mu{2}\right)}$$ For two normal distributions Obtain the appropriate point estimator

Normal distributions

### The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals. The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of$22.92. The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the store's brand of men's grooming products.

Normal distributions

### True or False: only the sums of normal distributions are also normal distributions.

Normal distributions

### Consider two normal distributions, one with mean-4 and standard deviation 3, and the other with mean 6 and standard deviation 3. Answer true or false to each statement and explain your answers. a. The two normal distributions have the same spread. b. The two normal distributions are centered at the same place.

Normal distributions

### Explain why t distributions tend to be flatter and more spread out than the normal distribution.

Normal distributions

### Basic Computation:$$\hat{p}$$ Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (b) Suppose $$n= 25$$ and $$p= 0.15$$. Can we safely approximate the $$\hat{p}$$ distribution by a normal distribution? Why or why not?

Normal distributions

### Why do two normal distributions that have equal standard deviations have the same shape?

Normal distributions

### The normal distribution is really a family of distributions. Is the standard normal distribution also a family of distributions?Explain.

Normal distributions

### Find the mean of standard normal distribution. Find the standard deviation of standard normal distribution.

Normal distributions

### A fair coin is flipped 104 times. Let x be the number of heads. What normal distributions best approximates x?

Normal distributions

### Basic Computation: hat p Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (b) Suppose $$n= 20$$ and $$p=0.23$$. Can we safely approximate the \hat{p} distribution by a normal distribution? Why or why not?

Normal distributions

### Basic Computation:$$\hat{p}$$ Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose $$n = 33$$ and $$p = 0.21$$. Can we approximate the $$\hat{p}$$ distribution by a normal distribution? Why? What are the values of $$\mu_{hat{p}}$$ and $$\sigma_ {\hat{p}}$$.?

Normal distributions

### (c) Give a brief outline describing how the sample size for a predetermined error tolerance and level of confidence is determined from the normal distribution.

Normal distributions

### Which of the following binomial distributions can be well approximated by a normal distribution? A Poisson distribution? Both? Neither? (с)$$n=500$$,$$p=.001$$

Normal distributions