SD - mean

The mean is 10 and the standard deviation is 3.5. If the data set contains 40 data values, approximately how many of the data values will fall within the range of 6.5 to 13.5?

Correct answer:

x =  40

Step-by-step explanation:

$$\begin{gathered} n=40 \\ m=10 \\ s=3.5 \\ D=13.5-6.5=7 \\ q=D\mathrm{/}s=7\mathrm{/}3.5=2 \\ x=0.6826\cdot 40=27.304=40 \end{gathered}$$

Try another example

Showing 3 comments:

Ivo

Rule 1 sigma for a normal distribution (from the average on both sides distance standard deviation sigma) lies 68.26% of the values, if are normally distributed.

5 years ago  Like

Math student

please I don't get the last part of the solution

3 years ago  Like

Dr Math

please use our normal distribution calculator:

https://www.hackmath.net/en/calculator/normal-distribution?mean=10&sd=3.5&above=&below=&area=between&ll=6.5&ul=13.5&outsideLL=&outsideUL=&draw=Calculate

3 years ago  Like

Related math problems and questions:

• Normal Distribution
  At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5?
• A mountain
  A mountain climber plans to buy some rope to use as lifeline. Which of the following would be the better choice? Explain your choice. Rope A: Mean breaking strength:500lb; standard deviation of 100lb Rope B: Mean breaking strength: 500lb; standard deviati
• Stoaches
  Stoaches are fictional creatures distantly related to bigfoot and yeti. Stoach weights are normally distributed, with mean 904g and standard deviation 104g. State the probability that the sample mean of a random sample of 36 stoach weights exceeds 943g. (
• Normal distribution GPA
  The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA?
• Assembly time
  The assembly time for the toy follows a normal distribution with a mean of 75 minutes and a standard deviation of 9 minutes. The company closes at 5 pm every day. If one starts assembling at 4 pm what is the probability that he will finish before the comp
• Performance comparing
  A standardized test was administered to thousands of students with a mean score of 85 and a standard deviation of 8. A random sample of 50 students were given the same test and showed an average score of 83.20. Is there evidence to show that this group ha
• Tallest people a
  As a group, the Dutch are amongst the tallest people in the world. The average Dutchman is 184 cm tall. If a normal distribution is appropriate, and the standard deviation for Dutchmen is about 8 cm, what is the percentage of Dutchmen who will be over 2 m
• A machine
  A machine produces steel rods of normally distributed length; the mean length and the standard deviation being 50.0 cm and 0.5 cm respectively. The rods do not conform to safety standards if they are either shorter than 49.1 cm or longer than 50.7 cm in l
• Standard deviation
  Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
• Statistical XY file
  Year; money spent on advertising; profit (three values each row) 2008 2 12 2009 5 20 2010 7 25 2011 11 26 2012 15 40 1. draw a scatter diagram depicting the data. 2. calculate the Pearson's correlation coefficient. 3. determine the linear regression equat
• Complaints
  The table is given: days complaints 0-4 2 5-9 4 10-14 8 15-19 6 20-24 4 25-29 3 30-34 3 1.1 What percentage of complaints were resolved within 2weeks? 1.2 calculate the mean number of days to resolve these complaints. 1.3 calculate the modal number of day
• Life expectancy
  The life expectancy of batteries has a normal distribution with a mean of 350 minutes and standard deviation of 10 minutes. What the range in minutes 68% of the batteries will last? What is the range in minutes approximately 99.7% of batteries will last?
• Tennis aces
  The number of aces served by Novak Djokovic in the last 20 tournaments that he has participated in, is shown below. 12 17 13 7 8 14 11 14 10 12 15 9 11 13 6 15 18 5 19 24 1.1 using the raw, determine the range. 1.2 Group the data into a frequency distribu
• Mixed numbers
  Rewrite mixed numbers, so the fractions have the same denominator: 5 1/5 - 2 2/3
• Unemployment rate
  Over the last 16 years, the country's unemployment rate has changed according to the following frequency table: years of unemployment: 2 5 2 3 3 1 unemploymen rate: 0.5 1 1.5 2 2.5 3 in % (percent). Determine the two-sided confidence interval for the vari
• Std-deviation
  Calculate standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90
• Simplify 3
  Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.