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Activity: Answer the following and illustrate each under the normal curve: 1. Compute the probability area to the left of z = -1.25. 2. Find the 90th percentile of a normal curve. 3. Find the probability area between z = -0.25 and z = 1.5. 4. In one Barangay of South Cotabato, there are 500 families who are members of SAP. Their mean of family members is 6 with a standard deviation of 2. a. How many families have 4 to 11 members? b. Find the percentage of families with more than 9.

Activity: Answer the following and illustrate each under the normal curve: 1. Compute the probability area to the left of z = -1.25. 2. Find the 90th percentile of a normal curve. 3. Find the probability area between z = -0.25 and z = 1.5. 4. In one Barangay of South Cotabato, there are 500 families who are members of SAP. Their mean of family members is 6 with a standard deviation of 2. a. How many families have 4 to 11 members? b. Find the percentage of families with more than 9.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please answer the question(s) with the same format as the examples. Thank you.

Example 1: Find the probability of the area below z= 0.50. Example 3: Find the 85th percentile of a normal distribution. Step 1: Draw appropriate normal curve. Step 1: Sketch the curve. 85% The probability that |Z<0.5 is equal to the shaded area Step 2: Express the percentage as probability. Step 3: Refer to the Table 85% is the same as .500 under the curve. This area is not found in the of Areas Under the Normal table. It is between 0.84849 (z = 1.03 and 0.85083 (z= 1.04). 0.5 Step 2: Consult the z= 0.50 corresponds to an area of z - Table and find the area that 0. 0.69146 Curve. Step 4: Find the average of the two z values. Step 5: Locate z=1.035 under the curve in step 1 and make a statement Step 6: Describe the shaded region _1.03+1.04_ 2.07 =1.035 corresponds to z = 0.50 Step 3. Make a statement indicating below z= 0.50 is 0.69146 or the required area. 2 The 85th percentile is z=1.035 Thus, the probability of the area The shaded region is 85% of the distribution. 69.146%. Example 2: Find the probability of the area between z = -1 The 85th percentile of the and 1.3. distribution is the shaded Step 1: Sketch the 85% region to the left of z=1.035 curve. as shown in the normal curve. 1.035 The probability that
Transcribed Image Text:Example 1: Find the probability of the area below z= 0.50. Example 3: Find the 85th percentile of a normal distribution. Step 1: Draw appropriate normal curve. Step 1: Sketch the curve. 85% The probability that |Z<0.5 is equal to the shaded area Step 2: Express the percentage as probability. Step 3: Refer to the Table 85% is the same as .500 under the curve. This area is not found in the of Areas Under the Normal table. It is between 0.84849 (z = 1.03 and 0.85083 (z= 1.04). 0.5 Step 2: Consult the z= 0.50 corresponds to an area of z - Table and find the area that 0. 0.69146 Curve. Step 4: Find the average of the two z values. Step 5: Locate z=1.035 under the curve in step 1 and make a statement Step 6: Describe the shaded region _1.03+1.04_ 2.07 =1.035 corresponds to z = 0.50 Step 3. Make a statement indicating below z= 0.50 is 0.69146 or the required area. 2 The 85th percentile is z=1.035 Thus, the probability of the area The shaded region is 85% of the distribution. 69.146%. Example 2: Find the probability of the area between z = -1 The 85th percentile of the and 1.3. distribution is the shaded Step 1: Sketch the 85% region to the left of z=1.035 curve. as shown in the normal curve. 1.035 The probability that
The 85 percentile of the Example 2: Find the probability of the area between z = -1 and 1.3. distribution is the shaded Step 1: Sketch the region to the left of z=1.035 85% curve. as shown in the normal curve. 0 1.035 The probability that -1<Z<1.3 is equal Activity: Answer the following and illustrate each under to the shaded area under the curve. the normal curve: 1.3 1. Compute the probability area to the left of z= -1.25. Step 2: Examine the graph and use probability notation P (-1<Z<l.3) = P (Z<1.3) – P(Z<-1) to form an equation showing the appropriate operation to get the P(-1<Z<1.3) = 0.90320 - 0.15866 required area. Step 3. Make a To find the probability of P (-1<Z<l.3), we use the following formula: 2. Find the 90th percentile of a normal curve. That is: 3. Find the probability area between z= -0.25 and z= P(Z<1.3) = 0.90320 and P(Z<-1)= 0.15866 1.5. 4. In one Barangay of South Cotabato, there are 500 = 0.74454 families who are members of SAP. Their mean of Thus, the probability of the area statement between z = -1 and z = 1.3 is 0.74454 family members is 6 with a standard deviation of 2. indicating the required area. or 74.454%. a. How many families have 4 to 11 members? b. Find the percentage of families with more than 9.
Transcribed Image Text:The 85 percentile of the Example 2: Find the probability of the area between z = -1 and 1.3. distribution is the shaded Step 1: Sketch the region to the left of z=1.035 85% curve. as shown in the normal curve. 0 1.035 The probability that -1<Z<1.3 is equal Activity: Answer the following and illustrate each under to the shaded area under the curve. the normal curve: 1.3 1. Compute the probability area to the left of z= -1.25. Step 2: Examine the graph and use probability notation P (-1<Z<l.3) = P (Z<1.3) – P(Z<-1) to form an equation showing the appropriate operation to get the P(-1<Z<1.3) = 0.90320 - 0.15866 required area. Step 3. Make a To find the probability of P (-1<Z<l.3), we use the following formula: 2. Find the 90th percentile of a normal curve. That is: 3. Find the probability area between z= -0.25 and z= P(Z<1.3) = 0.90320 and P(Z<-1)= 0.15866 1.5. 4. In one Barangay of South Cotabato, there are 500 = 0.74454 families who are members of SAP. Their mean of Thus, the probability of the area statement between z = -1 and z = 1.3 is 0.74454 family members is 6 with a standard deviation of 2. indicating the required area. or 74.454%. a. How many families have 4 to 11 members? b. Find the percentage of families with more than 9.
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