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)

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)

Solutions

Expert Solution

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


Related Solutions

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...
1. Suppose the variable x is represented by a standard normal distribution. What is the probability...
1. Suppose the variable x is represented by a standard normal distribution. What is the probability of x < -0.6? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12). 2. Suppose the variable x is represented by a standard normal distribution. What value of x is at the 90th percentile of the distribution? Equivalently, what is the value for which there is a probability of 0.90 that x...
Describe the point estimate, normal probability distribution, and standard normal probability distribution in details, in 4 paragraphs.
Empolyee age 1 25 2 32 3 26 4 40 5 50 6 54 7 22 8 23 age     Mean 34 Standard Error 4.444097209 Median 29 Mode #N/A Standard Deviation 12.56980509 Sample Variance 158 Kurtosis -1.152221485 Skewness 0.767648041 Range 32 Minimum 22 Maximum 54 Sum 272 Count 8 Confidence Level(95.0%) 10.50862004 Describe the point estimate, normal probability distribution, and standard normal probability distribution in details, in 4 paragraphs. 
(1) Consider a normal distribution with mean 38 and standard deviation 3. What is the probability...
(1) Consider a normal distribution with mean 38 and standard deviation 3. What is the probability a value selected at random from this distribution is greater than 38? (Round your answer to two decimal places.) (4) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 14.1; σ = 4.4 P(10 ≤ x ≤ 26)= (5) Assume that x has a normal distribution...
For a standard normal distribution, what is the probability that z is greater than 1.65
For a standard normal distribution, what is the probability that z is greater than 1.65
1. Following a normal probability distribution with a mean of 200 and a standard deviation of...
1. Following a normal probability distribution with a mean of 200 and a standard deviation of 10, 95 percent  of the population will be between: 200 and 220 180 and 220 180 and 200 less than 180 3. A family of four spends an average of $1000 per month with a standard deviation of $50.  This spending follows a normal continuous distribution.   What is the probability that a family will spend more than $1050 in a month?  (answer to 3 decimal places) 5....
9. For a standard normal distribution, what is the probability that Z is greater than -1.35?...
9. For a standard normal distribution, what is the probability that Z is greater than -1.35? Round to four decimals and use leading zeros. 10. For a standard normal variable, what is the probability that Z is between -2.00 and -1.00? Round to four decimals and use leading zeros. 11. For a dataset that follows the standard normal distribution, what is the probability that Z is between 2.00 and 3.00? Round to four decimals and use leading zeros.
2. Distributions a. For the standard normal probability distribution, what percent of the curve lies to...
2. Distributions a. For the standard normal probability distribution, what percent of the curve lies to the left of the mean? b. Describe a normal distribution and a standard normal distribution. c. You recently took a standardized test in which scores follow a normal distribution with a mean of 14 and a standard deviation of 5. You were told that your score is at the 75th percentile of this distribution. What is your score? d. The random variable X is...
Three cards are chosen at random from a standard deck of 52. What is the probability...
Three cards are chosen at random from a standard deck of 52. What is the probability that all three cards are hearts? What is the probability that all three cards are even? What is the probability that all three cards are hearts and even? What is the probability that all three cards are not aces? e) What is the probability of at least one ace?
What is a standard normal distribution?
What is a standard normal distribution? Give details explaination.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT