Question

# 2. Let the random variable Z follow a standard normal distribution, and let z1 be a...

2. Let the random variable Z follow a standard normal distribution, and let z1 be a possible value of Z that is representing the 10th percentile of the standard normal distribution. Find the value of z1. Show your calculation.

• A. 1.28
• B. -1.28
• C. 0.255
• D. -0.255

3. Given that X is a normally distributed random variable with a mean of 52 and a standard deviation of 2, the probability that X is between 48 and 56 is: Show your calculation.

• A. 0.0896
• B. 0.4104
• C. 0.9544
• D. 0.5896

Solution :

2 ) Given that,

Using standard normal table

P( Z < z1) = 10%
P(Z < z1) = 0.10

z1 = -1.28

Option b ) is correct.

3 ) Given that,

Using standard normal table

mean = = 52

standard deviation = = 2

P (48 < x < 56 )

P ( 48 - 52 / 2) < ( x - / ) < ( 56 - 52 / 2)

P ( - 4 / 2 < z < 4 / 2 )

P (-2 < z < 2 )

P ( z < 2 ) - P ( z < -2)

Using z table

= 0.9772 - 0.0228

=0.9544

Probability = 0.9544

Option c ) is correct.

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