Solution :
1)
P(Z > z) = 0.025
P(Z < z) = 1 - 0.025 = 0.975
P(Z < 1.960 = 0.975
z = 1.96
2)
P(Z > z) = 0.05
1 - P(Z < z) = 0.05
P(Z < z) = 0.95
P(Z < 1.65) = 0.95
z = 1.65
3)
P(Z > z) = 0.005
P(Z < z) = 1 - 0.005 = 0.995
P(Z < 2.8) = 0.995
4)
P(Z > z) = 0.01
P(Z < z) = 1 - 0.01 = 0.99
P(Z < 2.33) = 0.99
z = 2.33
probability Q7 (4 marks) a) Creat a standard normal probability distribution plot for z-value for the...
1. (5 points) Suppose Z is a random variable that follows the standard normal distribution. a) Find P(Z > 0.45). b) Find P(0.7 SZ 1.6). c) Find 20.09. d) Find the Z-score for having area 0.18 to its left under the standard normal curve. e) Find the value of z such that P(-2SZS2) -0.5.
1. (5 points) Suppose Z is a random variable that follows the standard normal distribution. a) Find P(Z > 0.45). b) Find P(0.7 SZ 1.6). c) Find 20.09. d) Find the Z-score for having area 0.18 to its left under the standard normal curve. e) Find the value of z such that P(-2SZS2) -0.5. 3. (4 points) The scores on a test are normally distributed with a mean of 75 and a standard deviation of 8. a) Find the proportion...
1. On the standard normal curve, find the following values of z. a. the value of z representing the 75th percentile or upper quartile b. the value of z representing the 15th percentile C, the value of z that cuts of the upper 25% of the area under the curve 2. Find the area under the standard normal curve to the left of 1.2 3. Find the area under the standard normal curve to the right of 2.48. 4. Find...
1) Given a standard normal distribution, find the probability of having a z score higher than 1.67 ```{r} ``` 2) Given that test scores for a class are normally distributed with a mean of 80 and variance 36, find the probability that a test score is lower than a 45. ```{r} ``` 3) Given a standard normal distribution, find the Z score associated with a probability of .888 ```{r} ``` 4) Find the Z score associated with the 33rd quantile...
In a normal distribution, the mean corresponds to: Standard Score: z = Percentile: Which of the following statements are TRUE about the normal distribution? Check all that apply. A data value with z-score = -1.5 is located 1.5 standard deviations below the mean. The mean corresponds to the z-score of 1. The Empirical Rule only applies when a value is exactly 1, 2, or 3 standard deviations away from the mean. A z-score is the number of standard deviations a...
Use the normal distribution of IQ scores, which has a mean of 105 and a standard deviation of 13, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity. Percentage of scores greater than 105 is _____ (Round to two decimal places as needed.) Standard score Percent -3 0.13 -2.5 0.62 -2 2.28 -1.5 6.68 -1 15.87 -0.9 18.41 -0.5 30.85 -0.1 46.02 0 50 0.1 53.98 0.5 69.15 0.9 81.59...
1 pts Z follows a standard normal distribution. What outcome, z (z-value), has a lower tail probability of 0.35?
Please show the work ! Find the value of Z for the standard normal distribution such that the area a) in the left tail is 0.1000 b) between 0 and Z is 0.2291 and Z is positive c) in the right tail is 0.0500 d) between 0 and Z is 0.3571 and Z is negative 1) 2) Find the following binomial probabilities using the normal approximation a) n- 70, p-0.30, P(x-18) b) n-200, p 0.70, P(133 x S 145) c)...
Chapter 06, Section 6.4, Go Tutorial Problem 037 Determine the value of z so that the area under the standard normal curve (a) in the right tail is 0.0275. Round the answer to two decimal places. (b) in the left tail is 0.0376. Round the answer to two decimal places.Chapter 06, Section 6.4, Additional Question 007 Use a table, calculator, or computer to find the specified area under a standard normal curve. Round your answers to 4 decimal places. a) More than a z-score of 2.48;...
Use the normal distribution of IQ scores, which has a mean of 125 and a standard deviation of 11,and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity. Percentage of scores greater than 152.5 is ___ % Standard score Percent -3 0.13 -2.5 0.62 -2 2.28 -1.5 6.68 -1 15.87 -0.9 18.41 -0.5 30.85 -0.1 46.02 0 50 0.1 53.98 0.5 69.15 0.9 81.59 1 84.13 1.5 93.32 2 97.72 2.5...