Question

In: Statistics and Probability

1. What is the probability that a value chosen from the standard normal distribution is less...

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

0.1949


0.02172. What is the probability that a value chosen from the standard normal distribution is greater than 2.02? (Keep 4 decimals)


0.24153. 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)

(a) P(X <= 214)9. Let X ~ N(189; 18). Find:


(b) P(146 < X < 203)

(c) The first quartile for X

(d) The third quartile for X

(e) the IQR for X

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

Solutions

Expert Solution

1:

Using z-table, the probability that a value chosen from the standard normal distribution is less than -0.86 is

Excel function used: "=NORMSDIST(-0.86)"

Answer: 0.1949

2:

The probability that a value chosen from the standard normal distribution is greater than 2.02 is

Answer: 0.0217

Excel function used: "=1 - NORMSDIST(2.02)"

3:

The probability that a value chosen from the standard normal distribution is between 0.44 and 1.35 is

Answer: 0.0217

Excel function used: "=NORMSDIST(1.35)-NORMSDIST(0.44)"

(4-5):

Using z-table or excel function "=NORMSINV(0.25)" the z-score -0.67 has approximately 0.25 area to its left.

Using z-table or excel function "=NORMSINV(0.75)" the z-score 0.67 has approximately 0.75 area to its left.

That is first quartile of standard normal distribution is and third quartile of standard normal distribution is .

6:

The median for the standard normal distribution is zero.

7:

The  IQR for the standard normal distribution is

orchestra answered 1 year ago
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