Question

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

Answer #1

Solution :

2 ) Given that,

Using standard normal table

P( Z < z_{1}) =
10%

P(Z < z_{1}) = 0.10

z_{1} = -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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