### Probability of Mean Test Scores Less Than 79 in Seaturtle Research StudiesA final exam in Seaturtle Research Studies has a mean of 78 and a standard deviation of 3. If 36 students are randomly selected, we aim to find the probability that the mean of their test scores is less than 79.#### QuestionGiven:- Mean ($\mu$) = 78- Standard deviation ($\sigma$) = 3- Number of students (n) = 36Find the probability $P(x < 79)$:\[ P(x < 79) = P\left(z < \frac{79 - \mu}{\frac{\sigma}{\sqrt{n}}} \right) = \]\[ P\left(z < \frac{79 - 78}{\frac{3}{\sqrt{36}}}\right) = P\left(z < \frac{1}{\frac{3}{6}}\right) = P(z < 2) \]Illustrate and calculate this probability using the standard normal distribution:#### Standard Normal Distribution ExplanationBelow is a standard normal distribution graph used to visually illustrate the probability:![Standard Normal Distribution](graph-url)- **Shaded Area**: The region to the left of $z = 2$ is shaded in blue.- **Meaning**: The shaded area represents $P(z < 2)$.- The arrow indicates the z-score of -1.5 corresponding to the 79 marks based on the standard normal distribution.#### InstructionsEnter your answer as a percentage accurate to 1 decimal place without the "%" sign.\[ P(z < 2) = \]Let's calculate the exact percentage and fill in the box:\[ P(z < 2) \approx 97.7\% \]Thus:\[ P(x < 79) = 97.7 \]Enter the value:\[ \boxed{97.7} \]Remember to use this calculator:Shade: Left of a value: $87.7$Click and drag the arrows to adjust the values to calculate the precise z-score related probabilities.

Answered: Image /qna-images/answer/c5da6f19-7e3a-4ebf-a1d0-ce22606c288b.jpg

A final exam in Seaturtle Research Studies has a mean of 78 and a standard deviation of 3. If 36 students are randomly selected, find the probability that the mean of their test scores less than 79. P(x < 79) = P(z < (Enter your answer as a percent accurate to 1 decimal place, do not enter the "%" sign). Shade: Left of a value Click and drag the arrows to adjust the values. -4 -3 -2 1 -1 0 1 2 3 4 -1.5

A final exam in Seaturtle Research Studies has a mean of 78 and a standard deviation of 3. If 36 students are randomly selected, find the probability that the mean of their test scores less than 79. P(x < 79) = P(z < (Enter your answer as a percent accurate to 1 decimal place, do not enter the "%" sign). Shade: Left of a value Click and drag the arrows to adjust the values. -4 -3 -2 1 -1 0 1 2 3 4 -1.5

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Find the mean and standard deviation for each group of numbers. Round answers to the hundredths place if necessary.(A) 12, 13, 15, 16, 24 (B) 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 15
Please type the solution
Scores on a test have a mean of 66 and a standard diviation of 9. Michelle has a score of 57. Convert Michelles score to z-score.
A simple data set has been provided to practice the basics of finding measures of variation. 2, 4, 8, 8 For the data set, determine the range and the sample standard deviation.
P-Value means
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Click to view page 1 of the table. Click to view page 2 of the table. The indicated IQ score, x, is (Round to one decimal place as needed.) A 0.55 X Q
Identify the line most likely to graphically represent the mean, median and mode of the distribution? Explain how you know. А: B: С: C A B
Compare the standard deviation of a data set when removing an outlier. An outlier is an extreme value that is significantly less or more than the rest of the data. During his 20 season NHL career, Wayne Gretzky scored more points than anyone who played professional hockey. He accomplished this feat while playing fewer games than the previous record holder. Here are the number of games Gretzky played during each season: 79, 80, 80, 80, 74, 80, 80, 79, 64, 78, 73, 78, 74, 45, 81, 48, 80, 82, 82, 70 Calculate the standard deviation with all his games and without his two lowest seasons. Compare the data. Rounding to the nearest hundredth, the difference between the standard deviation with and with out the outliers is
Assume that adults have IQ scores that are normally distributed with a mean of u = 105 and a standard deviation a = 15. Find the probability that a randomly selected adult has an IQ between 91 and 119. Click to view page 1 of the table. Click to view page 2 of the table. The probability that a randomly selected adult has an IQ between 91 and 119 is. (Type an integer or decimal rounded to four decimal places as needed.) Enter your answer in the answer box. MacBook Air esc 888 %23 & 2 3 4 5 6 7 8 Q E R T Y tab P A D G H caps lock K V в N M > ? control option command command option
A sample of 30 commuters in the area of a certain city yielded the accompanying commute times, in minutes. Preliminary data analyses indicate that the t-interval procedu interval for the mean commute time of all commuters in the area of the city. (Note: x= 27.47 minutes and s 9.81 minutes.) Click here to view the commute times. Click here to view page 1 of the t-table. Click here to view page 2 of the t-table. an reasonably be applied. Find and interpret a 99% confidence ..... The 99% confidence interval is from minute(s) to minute(s). (Round to one decimal place as needed.) Commute times 22 28 33 26 42 29 27 36 25 14 47 39 32 15 18 11 21 17 30 26 15 21 28 17 29 46 18 36 36 40 Print Done Clear all Check answer View an example Get more help - Help me solve this NOV W 3,769 étv 23 280 MacBook Air DII F11 F12 吕口 888 F10 • F7 F8 F9 F5 F6 F4 esc F2 F3 F1 & %23 %24 dele 7 8 9- 2 4. E R Y. 会 w/
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The area of the shaded region is. (Round to four decimal places as needed.) om/Player/Player.aspx?cultureld=&theme=math&style=highered&disableStandbyIndicator=true&assignmentHandlesLocale=true# NO REF SAMPLE....pdf 2 W S 5373255.docx X H ommand # 3 80 F3 E D $ A 4 C Q F4 R F % 01 % 5 V T G < 6 MacBook Air B Y TEMPLATE Sel....docx & 7 H F7 N * 8 J A DII FB 1 M 9 resume..docx K O < H db O L F10 P Clear all command - Л. : ; I { + [ = 80 option Check answer ? Show All I } A 1 G X dele
the mean is 7.0 the median is 6.5 , and the mode is 6.0 how would you describe this distribution in terms of skew (positive, negative , or no skew)