Standard Deviation given Variance?
Variance (σ²) = 225 Standard Deviation (σ) =? σ²=225 σ= √225 σ= 15....................answer
Scores are normally distributed with a mean of 86 and a standard deviation of 14. What is the probability that a random student scored below 72?
Hi,Use a Z Score calculator such as this one:Z Score or Standard Value CalculatorRandom Value = 72Mean (u) = 86Standard Deviation = 14You should get this resultUsing a Z Score lookup table:You will see a Z value of 1 = .3413 or 34.13% of the area under the curve.But… to finish the calculation we need to put all the numbers in the right context.The value of .3413 is the area under the curve from “0” (zero, the normalized average of 86) to the value of 100 or 72 (since normal distribution is symmetrical).The number you want is what is the probability of a random student getting a score below 72 (which is 1 standard deviation away from the average, by the way).What we need to do is calculate the percentage (probability) below 72 by subtracting .3413 from .5000 (.5000 is the probability of what is contained in the lower half of the normal distribution and the .3413 is the probability of what is above 72). So .5000 - .3413 = .1587 or the probability that a student scored below 72 is 15.87%.To calculate the probability of a student scoring 72 or better just add the probabilities above the 72 level which would be .3413 + .5000 (upper half of normal distribution which was not affected by our calculations) and we get .8413 or 84.13% probability a student scored above 72.I hope this helps…
The mean of a data is 10. If each observation is multiplied by 5 and then 1 is added to each result, how can you find the mean of the new observations obtained?
A2AMean = S/n (sum of all no.)S = a1+a2+….5*a1+ 5a2+… =5(a1+a2+..) = 5Sagain 1 is added t0 every no.hence ,5a1+1 +5a2+1 + 5a3+1 +….. n terms = 5(a1 + a2+ a3…) + 1+1+1… n terms = 5S +nnew mean = (5S+n)/n = 5* Mean + 1 = 51
10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of a combined set is given by?
10 is the mean for 7 observations so the total for those 7 observations is = 10*7 = 70Similarly, 5 is the mean for 3 observations so the total for those 3 observations is = 5*3 = 15Thus total for (7+3) = 10 observations = 70+15 = 85Mean = total/number of observations = 85/10 = 8.5
If students test scores are normally distributed (mean 75 and standard deviation 15), what is the probability that a randomly selected group of 10 students will have a mean score greater than 80?
[math]X_i =[/math] the mean of group [math]i[/math] of [math]10[/math] randomly selected students.[math]X[/math] is normally distributed with mean [math]= 75[/math], and standard deviation [math]= \frac{15}{\sqrt{10}}[/math][math]\begin{align*} P\left(X>80\right) & = \textstyle P\left(Z > \frac{80-75}{15/\sqrt{10}}\right) \\ & = 1 - \textstyle P\left(Z < \frac{\sqrt{10}}{3}\right) \\ & = 1 - 0.8541 \\ & = 0.1459 \\ & = \boxed{\boldsymbol{14.59\%}} \end{align*}[/math]
If I multiply the result of my observations by 3, how variance and mean will vary?
Mean will become three times while variance will become nine times. Std dev will become three times.MeanVariance
The mean of 10 observations was found to be 28. Later, it was discovered that one observation 14 was misread as 24. Find the correct mean? (A) 25 (B) 26 (C) 27 (D) 29
Mean =sum of observation ÷no. Of observationAccording to first statementSum=280As instead of 14,24 was misread,so we have to subtract 24 from 280280-24=256Then,we add correct observation i.e 14 in 256256+14=270Now , correct mean=270÷10=27So, correct mean is 27
The marks on a midterm test are normally distributed with a mean of 69 and a standard deviation of 10. What is the probability that a class of 27 has an average less than 67 (3 decimal places). How do I do this?
(I originally misread the question as 10 being the sample standard deviation)Your teacher probably wants you to answer this using a z-test. First, calculate the z score:z = [ sample mean - population mean ] / ( standard deviation of the population / square root of n )z = [ 67 - 69 ] / [ 10 / sqrt( 27 ) ]z = -1.04Then, look up this z-score in a z-score table (like this one: Page on utdallas.edu), and you get 14.92%.