If the GPA follows a normal distribution what is the 30th percentile GPA?

Q: A school psychologist is looking at assessment scores from the end of semester finals. She takes the…

A: (a) Step-by-step procedure to draw a curve for getting the probability of a sample mean of SEM=95…

Q: Heights of senior high women have a distribution that can be approximated by a normal curve with a…

A: Given: Mean=μ=60Standard deviation=σ=2.5Data points=x=65 and 67   The formula for z-score is…

Q: Ms. Hammell's Algebra 2 students took an exam. the results showed a mean of 78, with a standard…

A: The mean is 78, and standard deviation is 4. The Z-Score for 68% is, Z=X-μσ=68-784=-104=-2.5 Thus,…

Q: Please do provide explanation to the solutions. It will be much appreciated Thank you.  The time…

A: Given : Let, X be the time until recharge for a battery in a laptop computer. X~Nμ=260,σ2=502 And…

Q: he IQ of a person follows a normal distribution and has a mean of 100 and a standard deviation of…

A: Given that  The data is normally distributed with  Mean (μ) = 100 Standard deviation (σ) = 15   We…

Q: The scores on a psychology exam were normally distributed with a mean of 67 and a standard deviation…

A: Given Mean=67 andStandard deviation=7Cutoff=μ-2σ          =67-2*7          =67-14…

Q: The population average for SAT score is known to be 500 with a standard deviation of 100. this…

A: Given: μ=500σ=100n=15x¯=620 Hypothesis: Null hypothesis: H0: μ=500Alternative hypothesis: H1:…

Q: Consider a value to be significantly low if its z score less than or equal to - 2 or consider a…

A: It is given that the mean test score is 21.5 with standard deviation of 5.1. It is given that the…

Q: no handwriting please c) The amount of sodium sulfate, in mg, found in the soda follows a normal…

A: Given: Population meanμ=13Population standard deviationσ=2.5 Consider, X be the random variable that…

Q: Aña took both the SAT and the ACT before going to college. Her SAT verbal test had a mean of 500 and…

A:

Q: The scores on a test are normally distributed, with a mean of 82 and standard deviation of 8. What…

A: Followings are the Explanation of the question Use the Normal approximation method ( Z-score)…

Q: Find a raw score. What is the raw score? (

A: Here given,  The mean for a data set is 66. The standard deviation is 2 , and the z score is 0.55.

Q: A professor finds that the grades in a large class are normally distributed. The mean of the grades…

A: The percentiles in the normal distribution can be caclulated using the formula z=x-μσ. The value of…

Q: The rainfall in a town last year measured 61 inches. If the annual rainfall has a mean of 47.34…

A: given : mean ( u ) = 47.34 inches standard deviation ( σ ) = 12.75 inches measured rainfall ( x ) =…

Q: computer company claims that the employees' salary average = 6032 dollars. The standard deviation is…

A: Given information Hypothesized mean µ = 6032 dollars Sample size (n) = 36 Mean x̅  = 6123 Standard…

Q: What does it mean if the standard deviation of a given score is high? a) the scores are very low…

A: We know that,  For the normal distribution,  Z =( X- μ) /σ We can say that,   if the standard…

Q: Two friends enroll in the same math course at the university they are attending.  On the first exam…

A: Mean(µ) = 34 Standard deviations (σ) = 15 We have to find Sam's z-score

Q: The mean score of a college entrance test is 500; the standard deviation is 75. The scores are…

A: Given data: Mean = 500 Standard deviation = 75 X ~ N ( 500 , 75) To find: What percent of the…

Q: Consider a value to be significantly low if its z score less than or equal to -2 or consider a value…

A: Here, mean is 19.5 and standard deviation is 4.6.

Q: statistics that are useful for answering Using the standard deviation, we would expect two thirds of…

A: Here the standard deviation is 1.248 ad mean is 1.11

Q: Consider a value to be significantly low if its z score less than or equal to - 2 or consider a…

A:

Q: On a test the mean score is 25 and the standard deviation is 2.3.  Which score could be expected to…

A: Given information Mean µ = 25 Standard deviation σ = 2.3 P (Z< z) = 0.05 Z (0.05) = -1.6449…

Q: The mean height of a basketball team is 6 feet with a standard deviation of 0.2 feet. The team's…

A:

Q: In an Algebra class, the scores on a test are normally distributed. The middle 68% of the scores…

A: According to Empirical rule (68-95-99.7 rule) Given that the middle 68% of the scores fall…

Q: The mean weight of fish raised at the Stockton Fish Farm is 2.2 pounds. The standard deviation is…

A: Chebyshev's theorem: At least 1-(1/k2) of the values are lies between k standard deviations µ±kσ.…

Q: Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout.…

A: Givenaverage length of trout caught in Pyramid Lake is μ = 19 inches.Sample size = 45sample mean = x…

Q: Consider a value to be significantly low if its z score less than or equal to -2 or consider a value…

A: Given Mean, μ=20.5SD, σ=5.4

Q: Consider a value to be significantly low if its z score less than or equal to - 2 or consider a…

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

Q: Urgent need help immediately The average freshman GPA is 3.0 with a standard deviation of 0.4. If…

A: Given  mu=3, sigma=sd=0.4, P(X<a)=0.30 We want to find the value of "a"

Q: uppose you know that the amount of time it takes your friend Susan to get from her residence to…

A: It is given that the mean and standard deviation are 50 and 5, respectively.

Q: Consider a value to be significantly low if its z score less than or equal to - 2 or consider a…

A: A test score is considered to be significantly low if it is two standard deviations below the mean…

Q: The scores on a psychology exam were normally distributed with a mean of 56 and a standard deviation…

A:

Q: A professor told her class that the midterm scores were normally distributed. The average score in…

A:

Q: Adistribution has a mean of 40 and a standard deviation of 5. Approximately 95% of the distribution…

A:

Q: The population average for SAT scores is known to be 500 with a standard deviation of 100. This…

A: Null Hypothesis: A hypothesis which is tested for plausible rejection is called the Null Hypothesis…

Q: Consider a value to be significantly low if its z score less than or equal to -2 or consider a value…

A:

Q: In a normal distribution, 10% of the items are over 125 and 35% are under 60. Then the mean value is…

A: In a normal distribution, 10% of the items are over 125 and 35% are under 60.i.e.  P(X>125)=0.10…

Q: The sum of squared deviations for a data set drawn from a larger population is 1314. What additional…

A: Standard Deviation:

Q: Jason got 85 on Math 150 final exam. The scores of Jason's class have a mean of 82 and a standard…

A:

Q: Prospect Y = ($90, 0.25; $146, 0.75) What is the standard deviation of Prospect Y? (Note: The answer…

A: Given information: The probability distribution of the Prospect Y is as given below:

Q: Answer according to Swikness theorm. Thank you Illustration : The mean and standard deviation of a…

A:

Q: the mean height of a basketball team is 6 feet with a standard deviation of 0.2 feet. the team's…

A:

Q: Aña took both the SAT and the ACT before going to college. Her SAT verbal test had a mean of 500 and…

A: Given  Mean of SAT verbal test MSAT=500 Standard deviation of SAT verbal test SDSAT=100 Raw score in…

Q: Select the most appropriate response. One normal distribution has a mean of 34 and a standard…

A: The provided values of mean and sample standard deviation for both the distributions are:

Q: You want to estimate the sample standard deviation so you can get an idea of how large of a sample…

A: Given information Maximum number = 14 Minimum number = 4 Using Range rule of thumb, sample standard…

Q: A data set is normally distributed with a mean of 63 and a standard deviation of 10.4. What…

A: Solution-: Given: μ=63,σ=10.4 We find percentage of data is between 45 and 77?

Q: In an Algebra class, the scores on a test are normally distributed. The middle 68% of the scores…

A: Given information middle 68% of the scores fall between 69 and 81 As per empirical rule 68% of data…

Q: InACULATE CO 2. In an English test, the mean is 60 and the standard deviation is 6. Assuming the…

A: Given,mean(μ)=60standard deviation(σ)=6

Q: Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout.…

A: Hey, since there are multiple subparts posted, we will answer first three question. If you want any…

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!