A normal distribution has a mean of 50 and a standard deviation of 4. Please i want to determine the value below which 95% of the observations will occur.

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lamusesamuset · Accepted Answer

μ=50,&amp;nbsp;σ=4X - random variable, and we have formula for standard deviationz=X−μσ⇒z=X−504z1=X1−50495% of the observations lie below&amp;nbsp;X1.⇒P(z&amp;lt;z1)=0.95⇒0.5+P(0&amp;lt;z&amp;lt;z1)=0.95⇒P(0&amp;lt;z&amp;lt;z1)=0.95−0.5⇒P(0&amp;lt;z&amp;lt;z1)=0.45⇒z1=1.64z1=X1−504⇒1.64=X1−504⇒X1−50=6.56⇒X1=56.65Answer: 95% of the observations will lie below 56.65.

Don Sumner · Accepted Answer

Answer:In a normal distribution with a mean of 50 and a standard deviation of 4, the value below which 95% of the observations will occur is approximately 56.58.Explanation:The CDF gives us the probability that a random variable takes on a value less than or equal to a certain value. In this case, we want to find the value below which 95% of the observations occur, which means we need to find the point where the CDF equals 0.95.The CDF of a normal distribution with mean μ and standard deviation σ is denoted as Φ(x), where x is the value we want to find. Since the mean is 50 and the standard deviation is 4, we have μ=50 and σ=4. Therefore, we want to find x such that Φ(x)=0.95.Using a standard normal distribution table or a calculator, we can find the corresponding z-score for a cumulative probability of 0.95. The z-score is the number of standard deviations away from the mean. In this case, we want to find z such that Φ(z)=0.95.Now, we can calculate the z-score using the standard normal distribution table or a calculator. The z-score corresponding to a cumulative probability of 0.95 is approximately 1.645.To find the value x corresponding to this z-score, we can use the formula:x=μ+z·σSubstituting the values we have:x=50+1.645·4Simplifying the equation, we get:x=50+6.58Therefore, the value below which 95% of the observations will occur is approximately 56.58.

RizerMix · Accepted Answer

Given:The z-score formula is given by:z=x−μσwhere:- z is the z-score,- x is the value we want to determine,- μ is the mean of the distribution, and- σ is the standard deviation of the distribution.In this case, we want to find the value x below which 95% of the observations will occur. Since the normal distribution is symmetric, we can use the z-score corresponding to a 95% cumulative probability in the standard normal distribution, which is approximately 1.645.Substituting the given values into the z-score formula, we have:1.645=x−504To solve for x, we can rearrange the equation:x−50=1.645×4Simplifying further:x−50=6.58Finally, solving for x:x=50+6.58=56.58Therefore, the value below which 95% of the observations will occur is approximately 56.58.

nick1337 · Accepted Answer

To calculate the value below which 95% of the observations will occur, we can use the inverse cumulative distribution function (CDF) of the normal distribution, denoted as Φ−1.The formula for calculating the value corresponding to the 95th percentile is:Value&amp;nbsp;for&amp;nbsp;the&amp;nbsp;95th&amp;nbsp;percentile=μ+σ·Φ−1(0.95)Substituting the given values, we have:Value&amp;nbsp;for&amp;nbsp;the&amp;nbsp;95th&amp;nbsp;percentile=50+4·Φ−1(0.95)Now, let&#039;s calculate the value below which 95% of the observations will occur using the standard normal distribution table or a calculator:Value&amp;nbsp;for&amp;nbsp;the&amp;nbsp;95th&amp;nbsp;percentile≈50+4·1.645≈50+6.58≈56.58Therefore, the value below which 95% of the observations will occur in this normal distribution is approximately 56.58.

A normal distribution has a mean of 50 and a standard deviation of 4. Determine

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