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

Q: Given a normal distribution of the lengths of wing-spans of a certain butterfly has a mean of 20 mm…

A: It is given that the wing spans follow normal distribution with mean 20 and standard deviation 3.5.…

Q: For a standard normal distribution, find: P(z < c) = 0.7359 Find c rounded to two decimal places.

A: Solution

Q: For a standard normal distribution, find: P(z < c) = 0.8369 Find c rounded to two decimal places.

A: It is given that the P(z&lt;c) =0.8369.

Q: Given a normal distribution with mean of 67 and standard deviation of 5, the probability that X…

A: We have given that,  X be the random variable from normal distribution ,  Then, We have to check…

Q: Given a normal distribution with MEAN = 50 and SD = 10, find the probability that X assumes a value…

A:

Q: "Given a standard normal distribution with mean =114 and standard deviation = 26, find P(75 <X <…

A:

Q: Use the normal distribution of IQ​ scores, which has a mean of 105 and a standard deviation of 13​,…

A: GivenMean(μ)=105standard deviation(σ)=13

Q: A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the…

A: Given that a normal distribution has a mean of 20 and a standard deviation of 4.  We need to…

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 curve, find the probability a value has a z-score less than -2.

A: Standardized z-score:   The standardized z-score represents the number of standard deviations the…

Q: For a standard normal distribution, find: P(z > c) = 0.1116 Find c rounded to two decimal places.

A: Given that  P(z&gt;c)=0.1116 Z-score =(x-mu)/sigma

Q: If X has a normal distribution of a mean of 70 and a standard deviation of 10, then the area under…

A:

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

A:

Q: A normal distribution has a mean of 76 and a standard deviation of Determine the z-score for the…

A: Solution

Q: For a standard normal distribution, find: P(z < c) = 0.5467 Find c rounded to two decimal places

A: The normal distribution  in the center are generally denser and basically less denser at tails.…

Q: For a standard normal distribution, find: P(z < c) = 0.4879 Find c rounded to two decimal places.

A: P(Z &lt; c ) = 0.4879 Use Z- table or Excel function

Q: what is the probability that z is less than -0.21 or greater than the mean?

A: We want to find the probability that z is less than -0.21 or greater than the mean.

Q: For a standard normal distribution, use the Empirical Rule: P(z > 2) = _____ % answer as a decimal…

A: We know that empirical rule is also called as 68-95-99.7 percent rule. Empirical rule-

Q: A normal distribution is defined by two parameters, the mean and the __________. mode standard…

A: A normal distribution is defined by two parameters.

Q: For a standard normal distribution, find: P(z < c) = 0.8773 Find c rounded to two decimal places.

A: Here we need to find the value of c such that P(Z&lt;c)=0.8773 where Z~ N(0,1).

Q: Consider the standard normal distribution with mean = 0, and standard deviation  = 1

A: Given that  Standard deviation = 1 Mean = 0 Considering standard normal distribution.

Q: "Given a standard normal distribution with mean =146 and standard deviation = 42, find P(X<81)." A…

A:

Q: For a normal distribution with a mean of 60 and a standard deviation of 10 find the proportion of…

A: Solution: Let X be the score. From the given information, X follows normal distribution with a mean…

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: For a standard normal distribution, find: P(z < c) = 0.8343 Find c rounded to two decimal places.

A: Required probability is P(Z&lt;c)=0.8343

Q: "Given a standard normal distribution with mean =49 and standard deviation = 38, find P(X>95)."…

A:

Q: For a standard normal distribution, find: P(z > c) = 0.9693 Find c rounded to two decimal places.

A: From the provided information, P (z &gt; c) = 0.9693

Q: For a normally distributed random varible y, mean is 25 and standard deviation is 9. Find the z…

A:

Q: Given a normal distribution with mean 100 and standard deviation 10, find the number of standard…

A: Here, Mean is 100 and standard deviation is 10.

Q: for a standard normal distribution, find the percentage of data that are between 3 standard…

A: The graph with percentages is,

Q: "Given a standard normal distribution with mean =84 and standard deviation = 37, find P(X<119)."…

A:

Q: For a standard normal distribution, find: P(z < c) = 0.1134 Find c rounded to two decimal places.

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

Q: For a standard normal distribution, find: P(z > c) = 0.6193 Find c rounded to two decimal places.

A: Obtain the value of c such that P(Z&gt;c)=0.6193. The value of c is obtained below as follows:

Q: For a standard normal distribution, find: P(z < c) = 0.5776 Find c rounded to two decimal places.

A:

Q: For a normal distribution, find the percentage of data that are: a). Within 1 standard deviation of…

A: The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical…

Q: a normal distribution with a mean of Mean = 60 and a SD of 12, find the probability

A: Let us consider x is a random variable which follow normal distribution with mean = 60 and a SD of…

Q: For a standard normal distribution, find: P(z > c) = 0.8368 Find c rounded to two decimal places.

A: Solution: From the given information,

Q: Given a normal distribution with mean equal to 40 and a standard deviation of 6, find the value of x…

A:

Q: According to the Distribution of Z table, _______% of area under the normal curve is between the…

A: The random variable can be said to be follow standard normal distribution if the mean of the…

Q: Given a normal distribution with mean 100 and standard deviation​ 10, find the area under the normal…

A:

Q: "Given a standard normal distribution with mean =134 and standard deviation 38, find P(X>103)." A)…

A:

Q: A normal distribution has a mean of 77 and a standard deviation of 6. Find the z-score for a data…

A: z score: Consider X as a normally distributed random variable, with mean μ and standard deviation…

Q: "Given a standard normal distribution with mean =113 and standard deviation = 43, find P(X<58)."

A: Given:  random variable x from normal with mean =113 and standard deviations=43  then find the…

Q: Given a normal distribution with mean 25 and standard deviation 5, find the area under the normal…

A: Given mean 25 and standard deviation 5 We have to find the area between mean=25 to 36.1

Q: For a standard normal distribution, find: P(z > c) = 0.3075 Find c rounded to two decimal places.

A: We have to find C.

Q: For a standard normal distribution, find: P(z < c) = 0.6292 Find c rounded to two decimal places

A: Given that  P( Z &lt; c ) = 0.6292 By standard normal table of z

Q: "Given a standard normal distribution with mean =91 and standard deviation = 26, find P(90 < X %3D <…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: consider the normal distribution with mean 60 and standard deviation 12. Find the area under the…

A: Given that mean 60 and standard deviation 12. To find the area between [63,∞) 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!