Question

In: Statistics and Probability

Q9 Using the standard normal table, determine a z value (to the nearest two decimal places)...

Q9 Using the standard normal table, determine a z value (to the nearest two decimal places) such that the area [4 Marks] (a) From the midpoint to z is 0.20. (b) From the midpoint to z is 0.48. (c) Between z and negative infinity is 0.54. (d) Between z and positive infinity is 0.30.

DO NOT WRITE THE ANSWER - PLEASE USE WORD FORMAT.

Solutions

Expert Solution

The area under a standard normal curve is 1 with its value ranging from - infinity to + infinity with its midpoint at 0. So, the required values from the Z-table can be calculated as follows:

(a) Required z value is such that area under the curve between midpoint and z is 0.20. Now, in standard normal table if we want such an area we see the values that give area between negative infinity to z , in our problem we thus want

(b) The calculation is similar to that of (a) thus we need to find z such that area between negative infinity and z is 0.48+0.5= 0.98 so approximately .

(c) For this only the table is enough as it provides the required information directly.

(d)


Related Solutions

Find the z-score to the nearest two decimal places that: a) has 99.85% of the distribution's...
Find the z-score to the nearest two decimal places that: a) has 99.85% of the distribution's area to the right b) has .15% of the distribution's area to the left c) has 15% of the distribution's area to the right d) has 22.4% of the distribution's area to the left
Determine the standard normal (z) curve areas below. (Round all answers to four decimal places.) (a)...
Determine the standard normal (z) curve areas below. (Round all answers to four decimal places.) (a) The area under the z curve to the left of 1.74 (b) The area under the z curve to the left of -0.67 (c) The area under the z curve to the right of 1.3 (d) The area under the z curve to the right of -2.82 (e) The area under the z curve between -2.22 and 0.53 (f) The area under the z...
Determine the value z* that satisfies the conditions below. (Round all answers to two decimal places.)...
Determine the value z* that satisfies the conditions below. (Round all answers to two decimal places.) (a) Separates the largest 3.2% of all z values from the others z* =   (b) Separates the largest 0.8% of all z values from the others z* =   (c) Separates the smallest 5.6% of all z values from the others z* = (d) Separates the smallest 12.1% of all z values from the others z* =
Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)
  Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.) (a) The area to the left of z is 0.1841. (b) The area between −z and z is 0.9398. (c) The area between −z and z is 0.2052. (d) The area to the left of z is 0.9948. (e) The area to the right of z is 0.6915.
Using the z table (The Standard Normal Distribution Table), find the critical value (or values) for...
Using the z table (The Standard Normal Distribution Table), find the critical value (or values) for the two-tailed test with a=0.05 . Round to two decimal places, and enter the answers separated by a comma if needed.
1. Standard Normal Distribution P(z<c) = 0.7652 (two decimal places) 2. The mean score is 70,...
1. Standard Normal Distribution P(z<c) = 0.7652 (two decimal places) 2. The mean score is 70, standard deviation is 11, P(x>c) = 0.44 3. Out of 100 people sampled, 61 had kids. Construct a 90% confidence interval for the true population proportion of people with kids. __<p<__ (three decimal places) 4. P(-0.88<z<0.4) (four decimal places) 5. Mean of 1500, standard deviation of 300. Estimating the average SAT score, limit the margin of error to 95% confidence interval to 25 points,...
Between what two z-scores, to the nearest three decimal places, would we find (each question has...
Between what two z-scores, to the nearest three decimal places, would we find (each question has two answers as the question is asking for two z-score): a) 85.62% of the distribution's area?   b) 99.995% of the distribution's area?   c) 53.75% of the distribution's area?   d) 13.96% of the distribution's area? Please show your work! Any help is appreciated :)
Using the standard normal (z) distribution table, what is the area under the standard normal curve...
Using the standard normal (z) distribution table, what is the area under the standard normal curve between 1.67 and 2.72? a. 0.0442 b. 0.9525 c. 0.2563 d. 0.6140
Let z denote a variable that has a standard normal distribution. Determine the value z* to...
Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the following conditions. (Round all answers to two decimal places.) (a) P(z < z*) = 0.0244 z* =    (b) P(z < z*) = 0.0097 z* =   (c) P(z < z*) = 0.0484 z* =   (d) P(z > z*) = 0.0208 z* =   (e) P(z > z*) = 0.0097 z* =   (f) P(z > z* or z < −z*) = 0.2043 z* =
Calculate the following probabilities using the standard normal distribution. (Round your answers to four decimal places.)...
Calculate the following probabilities using the standard normal distribution. (Round your answers to four decimal places.) (a) P(0.0 ≤ Z ≤ 1.8) (b) P(−0.1 ≤ Z ≤ 0.0) (c) P(0.0 ≤ Z ≤ 1.46) (d) P(0.3 ≤ Z ≤ 1.58) (e) P(−2.02 ≤ Z ≤ −1.72) (f) P(−0.02 ≤ Z ≤ 3.51) (g) P(Z ≥ 2.10) (h) P(Z ≤ 1.63) (i) P(Z ≥ 6) (j) P(Z ≥ −9)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT