A random vanable X. has a nomal disrbution with mcan equalto 1000 and standard deviation equal to 100 The alue of X that ApprONinately t as17ofe area to the left is

Q: Ina random ample of males, it was found that 23 write with their left lun 217 de . In a random…

A: Given that: Use left-hand to write? Male Female Yes 23 65 No 217 455 Significance level,…

Q: Let x be a random variable that is noramlly distributed. Which of the following is not a propertu…

A: The question is about normal distribution Introduction : Let, X follows normal dist. with mean μ and…

Q: The total of the area to the left of zequals=negative 2.31−2.31 and the area to the right of…

A: The objective of this question is to find the total area under the standard normal curve to the left…

Q: 2. Find the value of z if the area under a standard normal curve (a) to the right of z is 0.4013;…

A: Standard normal distributionZ~N(0,1)Note : Area under standard normal distribution curve represents…

Q: 5.6 question attached!

A: Let X be the random variable, which follows gamma distribution.

Q: The area under the t-distribution with 18 degrees of freedom to the right of t= 1.56 is 0.0681. What…

A: Given that, The degrees of freedom are 18 The probability to the right of t=1.56 is 0.0681…

Q: Evaluate the integsal da a costx t6?Sin'x 2.

A: To evaluate: ∫0πxa2cos2x+b2sin2xdx Solution: Let I=∫0πxa2cos2x+b2sin2xdx…

Q: Find the sum of the areas under the standard normal curve to the left of z= -1.25 and to the right…

A:

Q: Find the area under the standard normal curve to the right of z=1.19 (b) Find the area under the…

A: It is given that the two different z-scores. Here, need to find out the area under these z-scores.…

Q: Find the z-score such that the area under the standard normal curve to the left is 0.44 (rounded to…

A: Here we need to find the z-score such that the area under the standard normal curve to the left is…

Q: Let x be a continuous random variable that follows a normal distribution with a mean of 218 and a…

A:

Q: An article reports that men over 6' tall earn more than man under 6' tall with these numbers average…

A:

Q: Find the area under the standard normal curve that les between the following two : values. Round…

A: As per bartleby guideline expert have to answer first three subparts only..

Q: Find the prob that the device does not faul before 17.6 days The gamma distribution with shape…

A: From the given information, the gamma distribution with shape parameter 5 and mean 11 of the time…

Q: The area under the standard normal curve from zero to z is 0.4505 and z is positive. The value of z…

A: Normal distribution is a symmetrical distribution so the area is equally distributed on both tails…

Q: 13: Find the​ Z-score such that the area under the standard normal curve to the left is o.52 .

A: Given: The area to the left of a particular z-score=0.52z-score=?

Q: consider the normal distrobution with mean 80 and standard deviation 5 find he area under the normal…

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Q: 4. For each z-score b X a) z=1.17 %3D X b) z =-1.37

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Q: The area under the curve of a chi square distribution X´(19) between 0 and Xá is 0.3, then Xá is…

A: It is given that, The area under the curve of chi-square distribution χ2(19) between 0 and χ2a is…

Q: About % of the area under the curve of the standard normal distribution (μ=0μ=0 and σ=1σ=1) is…

A: We have given that  The standard normal distribution (μ=0 and σ=1) is outside the interval Z =…

Q: 2. Given that Z is the standard NORMAL score, find and SKETCH: a) P (Z-1.6) c) P (-4<Z<1.96)

A: Let Z be the random variable from standard normal distribution with mean = 0 and standard deviation…

Q: i.e. P(>50) = P(X-9 olun But we know that Z=-4 oi√n - →210,1) = P(Z > Sone rivn from given data, ) =…

A: Given,sample size(n)=7mean(μ)=65.33standard deviation(σ)=31.59

Q: Please show your answer to 2 decimal places. About % of the area under the curve of the standard…

A: Z~N(0, 1) P(-0.66≤Z≤0.66)=? P(Z≤-0.66)= ? P(Z≥0.66)= ?  Note: We want to find the standard normal…

Q: Find the area between 23 and 25 under the normal distribution curve with x-bar=20 and s=4? Show…

A: Given data x-bar=20 s=4 we have to find p(23&lt;x&lt;25)

Q: Find the area under the t-curve to the right of  t = 2.539 (sample size n=20)

A: The sample size is, n = 20 The degree of freedom is, df=n-1   =20-1   =19

Q: Determine the area under the standard normal curve that lies to the right of -1.63. You must round…

A: Given, z=-1.63

Q: Find the area under the standard normal curve to the right of (z = 0). Answer:

A: We have to find given probability using z table.

Q: The area between a negative Z score and a positive Z score can be found by     adding the Z scores…

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: Determine the area under the standard normal curve that lies to the right of (a) Z=-0.63, (b)…

A: The question is about standard normal distribution Introduction : Standard normal distribution : It…

Q: Let x be a continuous random variable that has a normal distribution with a mean of 80 and a…

A: GivenMean(μ)=80standard deviation(σ)=12

Q: Which of the following is a continuous random variable Number of accident on highway Waiting time at…

A:

Q: Determine the area of under the Normal Curve for 20 area= [a]

A: Let Z be the random variable from normal distribution then we will find the area under normal curve…

Q: Find the area under the standard normal curve between two z values a) P(-1.96 2.575) c) P(z >…

A: Given problem Given that   Find the area under the standard normal curve between two z values

Q: Suppose the lengths of human pregnancies are normally distributed with μ=266 days and σ=16 days.…

A: Given that: Population mean, μ=266 Population standard deviation, σ=16

Q: About % of the area under the curve of the standard normal distribution (μ=0μ=0 and σ=1σ=1) is…

A: From the above data 38.43% of the area under the curve of the standard normal distribution (μ=0μ=0…

Q: The area under the Normal Distribution equals infinity 10 O 1 O 1

A: The normal distribution is a bell-shaped symmetric distribution with equal values of the mean, mode,…

Q: The total area to the left of zequals=negative 1.02−1.02 and to the right of zequals=1.621.62 under…

A: The objective of this question is to find the total area under the standard normal curve to the left…

Q: The area under the standard normal curve from 0 to -2.24 is ? Round to three decimal places as

A:

Q: find the Z- score such that the area under the standard normal curve to the right is 0.44 the…

A: From the provided information,The area under the standard normal curve to the right is 0.44.

Q: Find the area under the standard normal curve on the interval [-2.4, 2.4]. (Round your answer to…

A: The given interval is (-2.4, 2.4).

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!