In a normal distribution, a data value located 1.3 standard deviations below the mean has Standard Score: Z = In a normal distribution, a data value located 1.8 standard deviations above the mean has Standard Score: Z = In a normal distribution, the mean has Standard Score: z =

Q: For a normal distribution with a mean of 2 and a standard deviation of 0.5, what is p(1.7 < X <…

A: From the provided information, Mean (µ) = 2 Standard deviation (σ) = 0.5 X ~N (2, 0.5)

Q: For a standard normal distribution, find: P(-0.87 z<-0.03)

A: GivenP(-0.87&lt;z&lt;-0.03)

Q: For a standard normal distribution, find: P(z > c) = 0.6157 Find c.

A: Given data: For a standard normal distribution, find: P(z &gt; c) = 0.6157 Find c.

Q: Find P (x &gt; 3.24) for a standard normal distribution.

A: The standard normal distribution:A continuous random variable Z is said to follow standard normal…

Q: For a standard normal distribution, find: P(Z < 1.09)

A:

Q: For a standard normal distribution, find: P(-1.32 < z < -1.1)

A: The z scores are -1.32 and -1.1.

Q: For a standard normal distribution, find: P(z > c) = 0.981

A: From the provided information, P (z &gt; c) = 0.981

Q: For a standard normal distribution, find: P(z > c) = 0.9473 Find c.

A: The given probability is 0.9473.

Q: For a standard normal distribution, use the empirical rule to find: P(z < -2)=

A: Given, For a standard normal distribution, use the empirical rule to find P(Z&lt;-2)

Q: For a standard normal distribution , given P(z < c) = 0.6236

A: We have to find..... P(z &lt; c) = 0.6236

Q: In a normal distribution, what percent of the data lie a. within 3 standard deviations of the mean?…

A: As per empirical formula i) 68% of data falls within the first standard deviation from the mean. ii)…

Q: In a normal distribution whose mean=2 and standard deviation 3, (a) find the value of the variate…

A:

Q: For a standard normal distribution, find: P(z > c) = 0.715 Find c.

A: Given: Z has standard normal distribution Z~N0,1Pz&gt;c=0.715

Q: For a standard normal distribution, find: P(Z < 2.11)

A: The standard normal variable is z, which follows the normal distribution with the mean of 0 and…

Q: For a normal distribution with a mean of μ = 60 and a standard deviation of σ = 10, find the…

A:

Q: Given a normal distribution with μ = 35 and σ = 8, find: a. the normal curve area to the right of x…

A:

Q: determine the proportion of the standard normal distribution that lies between the following. z =…

A: Draw the normal curve and shade the area between z=-1.50 and z=1.50. The required shaded area under…

Q: For a normal distribution with a mean of μ = 85 and a standard deviation of σ = 20, find the…

A: 1. The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the…

Q: For a standard normal distribution, find: P(z > -2.34)

A: The objective is to find P(z &gt; -2.34)

Q: For a normal distribution with a mean of μ = 90 and a standard deviation of σ = 5, what is p(X>87)?…

A: We have given the following information about the normal distribution Mean = 90 Standard deviation…

Q: In a standard normal distribution, P(Z > 1.09) = a) 0.1379 b) 0.8621 c) 0.9713 d) 0.0287

A:

Q: A vertical line is drawn through a normal distribution at z- 080 What proportion of the distribution…

A: Standard Normal distribution.

Q: Assume that x has a normal distribution with the specified mean and standard deviation. Find the…

A:

Q: For a standard normal distribution, find: P(-2 < z < -0.09)

A: Normal distribution is a continuous distribution which has many real life applications. Normal curve…

Q: "Given a standard normal distribution with mean =80 and standard deviation = 36, find P(X>76)." A…

A: Given that  u = 80 Sigma  = 36 X = 76  Find P(x&gt; 76) = ???  By using standard normal…

Q: For a standard normal distribution, find: P(z < -0.21)

A: From the provided information, P (z &lt; -0.21)

Q: For a standard normal distribution, find: P(z < -1.29)

A: Draw the normal curve and shade the area to the left of z=-1.29.

Q: For a standard normal distribution, find: P(z > -1.25)

A:

Q: For a standard normal distribution, find: P(z < -1.56)

A: Given that, Z score = -1.56 (Left tailed)

Q: Given the normal distribution with a mean of 35 and a standard deviation of 6. Find the area: a.…

A: d. Suppose the variable of interest is X.

Q: Given a normal distribution with μ=30 and σ=6​, find​ (e) the two values of x that contain the…

A: It is given that the mean is 30 and the standard deviation is 6.

Q: Given a normal distribution with mean equal to 30 and standard deviation of 6, find the normal curve…

A: The mean of the data is 30. The standard deviation of the data is 6.

Q: The distribution of the sample mean IQ is a. exactly normal, mean 118, standard deviation 20. b.…

A: Hey there! Thanks for posting the question. However, we can answer only one question as per our…

Q: In a Normal Distribution with the Mean of 67 and the Standard Deviation of 5, find P (x < 60) A.…

A: The random variable X is normally distributed. The population mean is 67. The population standard…

Q: For a normal distribution with a population of  μ = 54 and a standard deviation of σ = 12, find the…

A:

Q: For a normal distribution with a mean of µ = 100 and a standard deviation of σ = 10, what is…

A:

Q: Given a normal distribution with mean 30 and standard deviation 5, the value of x that has a 40.52%…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: Consider a normal distribution curve where 60-th percentile is at 18 and the 45-th percentile is at…

A: Let X be the random variable that follows a normal distribution with the characteristics given in…

Q: In the standard normal distribution, the mean is equal to ______ and the standard deviation is equal…

A: We have find value of standard normal distribution..

Q: For a normal distribution with a mean of μ = 60 and a standard deviation of σ = 10, find the…

A: Given that, The proportion of the population corresponding to scores greater than 65 is,…

Q: For a standard normal distribution, find: P(z > 1.54)

A: We have to find p(z&gt;1.54)

Q: In a Normal Distribution with the Mean of 77 and the Standard Deviation of 5 , find P ( x>66)

A: Given,   Mean = 77 Standard deviation = 5   The objective is to find P ( x&gt;66)

Q: For a standard normal distribution, find: P(z< 1.7)

A: the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2standard normal distribution is a…

Q: For the standard normal​ curve, find the​ z-score that corresponds to the 90th percentile.…

A:

Q: For a standard normal distribution, find: P(z > -1.13)

A:

Q: The mean score of a competency test is 72, with a standard deviation of 5. Use the empirical rule to…

A: Empirical Rule: 68% of the values lies within one standard deviation from the mean. 95% of the…

Q: For a standard normal distribution, find: P(0.81 <z< 1.44)

A: the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2standard normal distribution is a…

Q: Given Z = X-μ/σ, what is the mean and standard deviation value, respectively of a standard normal…

A: We have given that,  Given Z = X-μ/σ, what is the mean and standard deviation value, respectively of…

Q: In a standard normal distribution, the range of values of z is from

A: For above 5. ASWSBE14 6.TB.2.015 The range of values of z is always between minus infinity and…

Q: For a standar normal distribution, find P(z <-1.05)

A: Given information- We have given a standard normal distribution. P (z &lt; -1.05) We have to find…

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!