Let X be a normal random variable with mean 199 units and standard deviation 6 u
ID: 3221768 • Letter: L
Question
Let X be a normal random variable with mean 199 units and standard deviation 6 units. Answer the following questions, rounding your answers to two decimal places: (a) What is the probability that X will be within 13 units of the mean? (b) The probability is 0.09 that X will be more than how many units? Assume that women's weights are normally distributed with a mean given by mu=143 lb and a standard deviation given by sigma=29 lb:... If 74 women are randomly selected, find the probability that they have a mean weight below 113?
Explanation / Answer
X be a normal random variable with mean 199 units and standard deviation 6 units.
µ = 199 and = 6
Applying transformation into standard normal variate we can solve this problem.
SNV = Z = (X - µ)/
(a) What is the probability that X will be within 13 units of the mean?
= P [ 186 < x < 212]
= P[(186-199)/6 < Z < (212-199)/6]
= P [ -2.17 < Z < 2.17]
Using normal distribution table we can find the probabilities
= 2 * Area between zero to 2.17 [Since normal distribution is symmetrical]
= 2*0.4850 = 0.97
Therefore, the probability that X will be within 13 units of the mean is 0.97.
(b) The probability is 0.09 that X will be more than how many units?
Appling the values in SNV
We have to find the value of x
P[X > 199] = 0.09
From normal distribution table, the correponding value of z is 1.34
Therefore, (X -199)/ 6 = 1.34
which gives x = (1.34*6) + 199 = 207.
Therefore the X will be more than 207 units to have the probability of 0.09.
Assume that women's weights are normally distributed with a mean given by mu=143 lb and a standard deviation given by sigma=29 lb:... If 74 women are randomly selected, find the probability that they have a mean weight below 113?
Answer:
µ = 143 and = 29
Probability that they have a mean weight below 113 = P [ x < 113]
= P [z < (113-143)/29]
= P[z < -1.0345]
Using normal distribution table,
= Area from -infinity ot zero - Area from zero to -1.0345
= 0.5 - 03485
= 0.1515
Therefore, Probability that they have a mean weight below 113 is 0.1515.
For, 74 women,
=74 * 0.1515 = 11.211 ~ 11
11 women will have weight below 113.
Hope this will help.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.