A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute

Tahmid Knox 2021-10-17 Answered
A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute the probability of a value 75.0 or less.

Want to know more about Probability?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

gotovub
Answered 2021-10-18 Author has 24253 answers

Mean of the normal distribution is \mu = 80 and the standard deviation is \(\displaystyle\sigma={14}\)
Let X be the random variable.
\(\displaystyle{P}{\left({X}{<}{75}\right)}={P}{\left({X}-\mu{<}{75}-\mu\right)}\)
\(\displaystyle={P}{\left({\frac{{{X}-\mu}}{{\sigma}}}{<}{\frac{{{75}-\mu}}{{\sigma}}}\right)}\)
\(\displaystyle={P}{\left({z}{<}{\frac{{{75}-{80}}}{{{14}}}}\right)}\)
\(\displaystyle={P}{\left({z}{<}{\frac{{-{5}}}{{{14}}}}\right)}\)
=P(z<-0.357)
=P(z>0.357)
=0.5-P(0 =0.5-0.14-6 (from Appendix B1.)
=0.3594

Not exactly what you’re looking for?
Ask My Question
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-03
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is \(\displaystyle\sigma={15}\)
a) Compute the \(\displaystyle{95}\%\) confidence interval for the population mean. Round your answers to one decimal place.
b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a \(\displaystyle{95}\%\) confidence interval for the population mean. Round your answers to two decimal places.
c) What is the effect of a larger sample size on the interval estimate?
Larger sample provides a-Select your answer-largersmallerItem 5 margin of error.
asked 2021-10-27
A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute the probability of a value between 55.0 and 70.0.
asked 2021-10-13
A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute the probability of a value between 75.0 and 90.0.
asked 2021-08-22
At Western University the historical mean of scholarship examination scores for freshman applications is 900. Ahistorical population standard deviation \(\displaystyleσσ={180}\) is assumed known.
Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a. State the hypotheses.
b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean \(\displaystyle{x}‾{x}\)= 935?
c. Use the confidence interval to conduct a hypothesis test. Using \(\displaystyleαα={.05}\), what is your conclusion?
d. What is the p-value?
asked 2021-11-19
The mean of a normal probability distribution is 60; the standard deviation is 5. a. About what percent of the observations lie between 55 and 65? b. About what percent of the observations lie between 50 and 70? c. About what percent of the observations lie between 45 and 75?
asked 2021-09-07
Assume a binomial probability distribution has p = 0.80 and n = 400.
a) what is the mean and standard deviation
b) is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.
c) what is the probability of 300 to 310 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question
...