State the approximate probability that a normal random variable will fall within the following intervals:Mean plus or minus one standard deviation

Let’s say the random variable X is normally distributed with a mean (µ) = 35 and standard deviation (σ) = 5. Can you find P(25 < X < 45), i.e., the probability of the variable falling between 25 and 45? Note 1: Report the answer as a number rounded off to two digits after the decimal point.Note 2: You’re not expected to know the right answer at this. This question is given just to get you thinking in the right direction

If all possible samples of size 16 are drawn from a normal population with mean equal to 50 and standard deviation equal to 5, what is the probability that a sample mean X¯ will fall in the interval from μX¯ −1.9σX¯ to μX¯ −0.4σX¯ ? Assume that the sample means can be measured to any degree of accuracy.

What is the probability that a normal random variable will take a value that is less than 1.05 standard deviations above its mean? In other words, what is P(Z < 1.05)?0.85310.14680.93320.0668What is the probability that a normal random variable will take a value that is between 1.5 standard deviations below the mean and 2.5 standard deviations above the mean? In other words, what is P(−1.5 < Z < 2.5)?0.99380.06680.92700.0730What is the probability that a normal random variable will take a value that is more than 2.55 standard deviations above its mean? In other words, what is P(Z > 2.55)?0.99450.99460.00550.0054

What is the probability that a normally distributed random variable lies within 1.65 standard deviations of the mean?Note: You can use the Z table here.95%90%85%80%

Normal VariablesWhat is the probability of a normally distributed random variable lying within 1.65 standard deviations of the mean?