Question

1. What is the probability that a value chosen from the standard normal distribution is less than -0.86? (Keep 4 decimals)

2. What is the probability that a value chosen from the standard normal distribution is greater than 2.02? (Keep 4 decimals)

3. what is the probability that a value chosen from the standard normal distribution is between 0.44 and 1.35? (Keep 4 decimals)

4. Find Q1 for the standard normal distribution. (Keep 2 decimals)

5. Find Q3 for the standard normal distribution. (Keep 2 decimals)

6. Find the median for the standard normal distribution. (Keep 2 decimals)  

7. Find IQR for the standard normal distribution. (Keep 2 decimals)

8. P(|Z|> 1.01)

9. Let X ~ N(189; 18). Find:

(a) P(X <= 214)

(b) P(146 < X < 203)  

(c) The first quartile for X

(d) The third quartile for X

(e) the IQR for X

(f) P(|X-189|> 37)

10. A soft drink machine discharges an average of 360 ml per cup. The amount of drink is normally distributed with standard deviation of 25 ml. What fraction of cups will contain more than 391 ml? (Keep 4 decimals)

Answer 1

Solution:

1)

The problem with the standard normal distribution is that it only provides the probability for positive z-values. So we will use the following formula:

Therefore, the probability that a value is chosen from the standard normal distribution is less than -0.86 is 0.1949

2)

The probability that a value chosen from the standard normal distribution is greater than 2.02 can be calculated as:

Therefore, the probability that a value is chosen from the standard normal distribution is greater than 2.02 is 0.0217

3)

the probability that a value chosen from the standard normal distribution is between 0.44 and 1.35 can be calculated as:

Therefore, the probability that a value is chosen from the standard normal distribution is between 0.44 and 1.35 is 0.2415