# What mathematician was instrumental in the creation of the normal distribution? What application prompted this person to create the normal distribution? Question
Normal distributions What mathematician was instrumental in the creation of the normal distribution? What application prompted this person to create the normal distribution? 2020-11-07
Carl Fredrich gauss was instrumental in creation of normal distribution. Due to his keen interest in mathematics of astronomy to obtain the orbit of a planetoid named Ceres, he used method of least squares which is a technique for experimental error.
In this method, x represents the error between true value and the value which obtained by experiment.
While theorizing the probability of a small error higher than that of a larger error Gauss came up with normal distribution to explain the probabilities of the random errors.

### Relevant Questions 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. 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.
(c) Suppose $$n = 48$$ and $$p= 0.15$$. Can we approximate the $$\hat{p}$$ distribution by a normal distribution? Why? What are the values of $$\mu_{hat{p}}$$ and $$\sigma_{p}$$.? 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 $$\sigma_ {\hat{p}}$$.? Select all that apply. We show that our sample statistics have (at minimum) a somewhat normal distribution because
this allows us to use t and z critical values.
this allows us to use t and z tables for probabilities.
this tells us that our sampling is appropriate.
normal distributions are cool and that's all we talk about in this class. A statistic is an unbiased estimator of a parameter when (a) the statistic is calculated from a random sample. (b) in a single sample, the value of the statistic is equal to the value of the parameter. (c) in many samples, the values of the statistic are very close to the value of the parameter. (d) in many samples, the values of the statistic are centered at the value of the parameter. (e) in many samples, the distribution of the statistic has a shape that is approximately Normal. (b) Give a brief outline describing how the normal approximation to the binomial distribution is used in the construction of confidence intervals for a proportion p. 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? (b) Suppose $$n= 20$$ and $$p=0.23$$. Can we safely approximate the \hat{p} distribution by a normal distribution? Why or why not? (a) Suppose $$n = 100$$ and $$p= 0.23$$. Can we safely approximate the \hat{p} distribution by a normal distribution? Why?
Compute $$\mu_{hat{p}}$$ and $$\sigma_{hat{p}}$$. 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?