Z- score multiple choice practice questions

1. The probability that a titanoboa is 120 feet long or longer is 0.0062 while the probability that it is less than 86 feet long is 0.0401. The mean length and standard deviation of a titanoboa are;

• mean = 2.5, Std dev = 0.5
• mean = 8, std dev = 100
• mean = 100, std dev = 8
• mean = 0.062, std dev = 0.0401
• Trick question!We need the z-scores to answer this!

2. If a random variable X~N(24, 16) and z = 1.75, then x = ___

• 31
• 17
• 20
• 28

3. Suppose P(X < a) = 0.8665, then P (X > -a) =

• 0.1335
• 0.8665
• 0.5
• Unknown, we need the z-score to do this.

4. If X~N(-6, 9) then P(X > -7) = ,

• 0.3703
• 0.6293
• 0.6179
• 0.5910

5. Suppose X~N(30,16). which of the following probabilities is the same as P(X>33)?

• P(X> 1- 33)
• P(Z > 33)
• P(Z = 33)
• P(Z < -0.75)

6. If z = 1.25, X = 16 and the mean of X is 10, then the standard deviation is,

• Unknown, we need the variance first
• 1.25
• 6
• 4.8
• 4

7. The z-score for a value P(Z < z) = 0.4721 is,

• -0.17
• 0.07
• -0.07
• None of the above.

8. Suppose I know that X~N(?, 16). If x = 26 and z = 1.5 then the mean of this distribution is;

• 32
• 26
• 22
• 20

9. Suppose I know that for a certain z-score P(z< score) = 0.9265, then the z-score is

• z = 1.44
• z = 1.45
• z = 1.55
• z = 1.35

10. If X~N(40, 100) then P(35 < X < 57.5) =

• 0.9599
• 0.6514
• 0.3085
• None of the above

11. Suppose the heights of Ice Gnomes are normally distributed with a mean height of 40 cm and a standard deviation of 2.5 cm. The probability that an Ice Gnome is between 37cm and 41.625cm tall is;

• 0.1151
• 0.7422
• 1.85
• .6271
• None of the above.

12. A random variable, X, is normally distributed with a mean of 60 and a standard deviation of 5. A value of X = 66 would be _______ standard deviations _______ the mean.

• 5, below
• 1.2, below
• 1.2, above
• 6, above