A population is normally distributed with µ = 86 and σ = 12. For this population, what is the 78th percentile?

Q: For a sample of n = 30 scores, a score that is 6 points above the mean has a z-score of z = 1.50.…

A: For a sample of n = 30 scores, a score that is 6 points above the mean has a z-score of z = 1.50.

Q: 4. Consider the Normal Gaussian distribution. How many data points would you need to take for a…

A: Given that we have to Consider the Normal Gaussian distribution.   We have to find how many data…

Q: Suppose a variable is Normally distributed with μ=345 and \sigma σ=30. What proportion of the data…

A: Mean(µ) = 345Standard deviations (σ) = 30X ~ N (µ, σ )= N(345, 30)

Q: For a normally distributed population with a mean of 35 and a standard deviation of 7.5 find P(X…

A: Solution:From the given information, normal distribution with population mean as 35 and standard…

Q: 24. For a sample with a mean of M = 51, a score of X = 59 corresponds to z = .00. What is the sample…

A: Given that mean, M= 51 Score, X= 59  And z Score= 2  We've to find sample standard deviation. We…

Q: Based on the graph of this normal distribution, a. The mean is b. The standard deviation is c. 68%…

A:

Q: From a normally distributed population, we took a simple random sample of 700 students with a mean…

A: Sample size n=700 Sample mean x¯=640 Population Standard deviation σ=300

Q: 15. For a population with a mean of p= 45, a score of X 54 corresponds to z = 1.50. What is the…

A: The population standard deviation is obtained below: From the given information, the value of mean…

Q: In a sample distribution, X=56 corresponds to z=1.00, and X=47 corresponds to z=-0.50. Find the mean…

A: Given,  X=56 corresponds to z=1.00 X=47 corresponds to z=-0.50 wktz=x-μσX=zσ +μ

Q: Can you find the standard deviation for sx and sy?

A:

Q: Given a population where p = 0.10, find the standard deviation of the samping distribution when n =…

A: It is given that p is 0.10 and n is 500.

Q: For a sample with a standard deviation S= 12, a score of X = 44 corresponds to a z = -1.00. What is…

A: The z-score of a random variable x is defined as follows: z = (x – x̅)/s. Here, x̅ and s are the…

Q: For a distribution in which X = 100, SX = 16, and N = 500 How many subjects are expected to score…

A: The number of subjects expected to score above 76 is,

Q: Given population parameters for two populations, population 1 has a mean of 800 and a standard…

A: Given that  Population 1  Mean (μ1) = 800 Standard deviation (σ1) = 40 Population 2 Mean (μ2) =…

Q: For example with m= 80, a score of x = 88 corresponds to z = 2.00.  What is the sample standard…

A: GivenMean(M)=80x=88z-score(z)=2.00

Q: A group of students take a Statistics Exam where the average was M = 90 and the standard deviation…

A:

Q: For a normally distributed population with a mean of 35 and a standard deviation of 7.5 find P(X…

A: Given dataMean = 35Standard deviation = 7.5

Q: For a normally distributed population with a mean of 35 and a standard deviation of 7.5 find P(X <…

A:

Q: Given a normally distributed population with a mean of 100 and variance 100, find f) P(90 Sx S 115)…

A: Let X be the random variable from normal distribution with mean (μ) = 100, variance (σ2)= 100 Then,…

Q: A population of scores has a mean of µ = 29, a median of 30, and a mode of 31. What is the most…

A: HERE FROM GIVEN INFORMATION MEAN = 29 MEDIAN = 30 MODE =31

Q: For a t distribution with 15 degrees of freedom, 90% of the distribution is within how many standard…

A:

Q: From a normally distributed population, we took a simple random sample of 700 students with a mean…

A:

Q: If x is normally distributed with a mean of 6 and a standard deviation of 4, find P(x>8) a. 0.1915…

A: If x is normally distributed with a mean of 6 and a stnadard deviation of 4, find Px&gt;8 Answer: b.…

Q: Assume a poison distribution if A = 3.7, find P(x=0) A represents a

A: We have given that,  Let X be random variable from Poisson distribution and A = 3.7, which is a…

Q: Given a population where p = 0.10, find the standard deviation of the samping distribution when n =…

A: It is given that p is 0.10 and n is 2,000.

Q: A sample has a mean M = 55. In the sample, a score of X = 48 corresponds to z = -1.50. What is the…

A:

Q: Given that the variances of random variables X and Y are 1600 and 900, respectively. The correlation…

A: Variance of a Random Variable: The variance of a random variable X, denoted by Var(X), is defined as…

Q: For a population with a standard deviation of o = 12, a score of X = 44 corresponds to z = -0.50.…

A:

Q: The scores on a driver's test are normally distributed with a mean of 100. Find the score that is 3…

A: From the provided information, Mean (µ) = 100 Standard deviation (σ) = 28 X~N (100, 28)

Q: For a population with a standard deviation of  sigma =12, a score of x=44 corresponds to z= -0.5.50.…

A: It is given that sigma is 12 and score, x is 44. Assuming that the z-score is –0.550. (Since it is…

Q: (d) adjusted coefficient of determination for each of the models in (a). Based on this measure,…

A: Reviewing information, n=No. of vehicles= 30 Y : Gas mileage of cars in MPG Var(Y)= 39.28

Q: A group of students take a Statistics Exam where the average was M = 90 and the standard deviation…

A:

Q: Given that it is normally distributed with a standard deviation of 8.025 cm. The engineer rejected…

A: we have to find mean value for given data...

Q: Given that s.e.(b) = 61 and the estimate is 32, what is the t-stat?

A: GivenSEβ=61Estimate(β)=32

Q: Given a scenario where n=100 and p=0.8, find the standard deviation.

A: In this case the sample size is n = 100 and p = 0.8.

Q: а. How many of the women have a height that is within 1 standard deviation of the mean? b. How many…

A:

Q: For a population with a standard deviation of s = 14, a score of X 5=24 corresponds to z = -0.50.…

A:

Q: A company has recorded data on the weekly sales for its product (y), the unit price of the…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: If you have a known value of 16, which of the following is the best average of your data to verify…

A: Here  We have given a known value of 16 if we go through the option and find their lower and upper…

Q: In a population distribution, a score of X = 28 corresponds to z = −1.00 and a score of X = 34…

A: Where, For X=28 &amp; z=-1.00 For X=34 &amp; z=-0.50

Q: Suppose a random variable X is best described by a normal distribution with =60 and et=14 Find the…

A: Given  Mean (mu) = 60 Variance(σ2)= 144 Standard deviation(σ)=√144= 12 Raw score(x) = 96

Q: In a population with m=60, a score of X=58 corresponds to a z-score of z=-0.50. What is the…

A:

Q: Consider a normal distribution curve where 70-th percentile is at 11 and the 30-th percentile is at…

A: Given 70-th percentile is at 11, then…

Q: Given a normally distributed population with a mean of 100 and variance 100, find f) P(90 sx s 115)…

A: Disclaimer : “Since you have posted a question with multiple sub-parts, we will solve first three…

Q: f the standard deviation of a normally distributed population is 22.0 and we take a sample of size…

A: It is given that the standard deviation is 22.0 and the sample size is 4.

Q: For a population with mean of 50 and standard deviation of 8, what is the z-score that corresponds…

A: Given that , mean = μ = 50 standard deviation = σ = 8 x = 46

Q: You are given that X follows a Weibull distribution where alpha = 2.3 beta = 17.4 What is the…

A:

Q: Suppose that a population parameter is 0.4 and many samples are taken from the population. If the…

A:

Q: For a population with a standard deviation of σ = 12, a score of X = 44 corresponds to z = −0.50.…

A:

Q: The results of a nationwide aptitude test in mathematics are normally distributed with m=80 and…

A: Given: m = 80 s = 10

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!