given a standard normal distribution, find the area of the curve that lies
a.) to the right of z=1.84 and
b.) between z= -1.97 and z= 0.86
Answers
Step-by-step explanation:
1a. What is the area between z = 0 and z = 2.24?d
Answer: z=o Area= 0.5000 , z =2.24 Area= 0.9875
0.9875-0.5000=0.4875.
1b. What is the area to the left of z = 1.09?
Answer: left of z=1.09=0.8621
1c. What is the area between z = -1.15 and z = -0.56
Answer: z= -1.15 Area =0.1251 z= -0.56 Area= 0.2877
0.2877-0.1251= 0.1626
1d. What is the area to the right of z = -1.93
Answer: right of z= -1.93 Area (z=-1.93)=0.0268
1-0.0268= 0.9732
Section 5.2: Normal Distributions: Finding Probabilities
(References: example 1 and 2 page 253, end of section exercises 13 - 30 pages 257 - 259
2. The diameters of a wooden dowel produced by a new machine are normally distributed with a mean of 0.55 inches and a standard deviation of 0.01 inches. What percent of the dowels will have a diameter greater than 0.57?
(6 points)
According to question we have to draw diagram. Diagram are in attachment
Answer are as follows:
(a) The area in figure (a) to the right of z=1.84 is equal to 1 minus the area in the table A.3 to the left of z=1.84 namely 1-0.9671=0.0329
(b) The area in figure between z=-1.97 and z=0.86 is equal to the area of left of z=0.86 minus the area of the left of z=-1.97 from table A.3 we find the desire area to be 0.8051-0.0244=0.7807
