contestada

Consider the population of all students in honors biology classes in the high school’s state who are given the task of using the spreadsheet program to investigate the topic in genetics. The distribution of the completion times has a shape similar to the combined histogram of students at the high school, with mean 70 minutes and standard deviation 26.5 minutes. For random samples of 50 students taken from the population, describe the sampling distribution of the sample mean completion time.

Respuesta :

The following are basic points

Explanation:

a)  The Group R have no experience, hence they need more time to complete

the Histogram II is appropriate for them as more data is to the right, where more time is taken

b)  if we combine it will be something like below

c)  n = 70 > 30 , hence bythe central limit theorem

The standrad normal distribution formula is used, mu is taken as 70 and whereas standard deviation is 26.5 as given in the question.

MrRoyal

A distribution may or may not follow a standard normal distribution.

The sampling distribution of the sample mean is standard normal distribution.

The given parameters are:

  • The population mean [tex]\mu = 70[/tex]
  • The standard deviation [tex]\sigma = 26.5[/tex]
  • The sample size, [tex]n = 50[/tex].

The population mean (70) is greater than 30.

So, we can make use of the central limit theorem.

Using the central limit theorem, we calculate the z-score using the following formula:

[tex]z= \frac{\bar x - \mu}{\sigma /\sqrt{n}}[/tex]

So, we have:

[tex]z= \frac{\bar x - 70}{26.5/\sqrt{50}}[/tex]

[tex]z= \frac{\bar x - 70}{26.5/7.1}[/tex]

This gives

[tex]z= \frac{\bar x - 70}{3.7}[/tex]

For whatever value, the sample mean has, the sampling distribution of the sample mean is standard normal distribution.

Read more about sampling distribution at:

https://brainly.com/question/12892403

Otras preguntas