If and are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that and are independent of each other, then P( and < 60) is:

A) .0401
B) .0802
C) .2115
D) .0016
E) .1255

Question

If

If and are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that and are independent of each other, then P( and < 60) is: A) .0401 B) .0802 C) .2115 D) .0016 E) .1255

and

are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that If and are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that and are independent of each other, then P( and < 60) is: A) .0401 B) .0802 C) .2115 D) .0016 E) .1255

and

are independent of each other, then P( If and are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that and are independent of each other, then P( and < 60) is: A) .0401 B) .0802 C) .2115 D) .0016 E) .1255

and

< 60) is:

A) .0401
B) .0802
C) .2115
D) .0016
E) .1255

Joshua Jimenea · Accepted Answer

Final Answer : D, Explanation :  We know that   and   are independent, so we can treat them as two separate normally distributed random variables.First, we need to find the z-score for a value of 60, using the formula:z = (x - μ) / σz = (60 - 95) / 20z = -1.75Next, we use a standard normal distribution table to find the probability of a z-score less than -1.75.This probability is 0.0401, which is equivalent to P(   < 60).Since  is also normally distributed with a mean of 95 and a standard deviation of 20, we can use the same process to find the probability of   < 60. This probability is also 0.0401.Because the two events are independent, we can multiply their probabilities to find the probability that they both occur:P( and   < 60) = P(   < 60) * P(  < 60)P(  and   < 60) = 0.0401 * 0.0401P(  and   < 60) = 0.0016So the answer is D.

If and are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that and are independent of each other, then P( and < 60) is:

A) .0401
B) .0802
C) .2115
D) .0016
E) .1255

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Learning Objectives

Learning Objectives

Related questions

If and are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that and are independent of each other, then P( and < 60) is:A) .0401B) .0802C) .2115D) .0016E) .1255

Definitions

Learning Objectives

Learning Objectives

Related questions

If and are normally distributed random variables with a mean of 95 and a standard deviation of 20, and that and are independent of each other, then P( and < 60) is:

A) .0401
B) .0802
C) .2115
D) .0016
E) .1255