Question

In: Statistics and Probability

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 normally distributed with a mean of 14 and a standard deviation of 5. What is the probability that a value of X chosen at random will be between 7.5 and 18.5?

Solutions

Expert Solution


Related Solutions

Given a standard normal distribution, find the area under the curve that lies (a) to the...
Given a standard normal distribution, find the area under the curve that lies (a) to the right of z=1.25; (b) to the left of z= -0.4; (c) to the left of z= 0.8; (d) between z=0.4 and z=1.3; (e) between z= -0.3 and z= 0.9; and (f) outside z= -1.5 to z= 1.5.
(a) Given a standard normal distribution, find the area under the curve that lies between z...
(a) Given a standard normal distribution, find the area under the curve that lies between z = −0.48 and z = 1.74. (b) Find the value of z if the area under a standard normal curve between 0 and z, with z > 0, is 0.4838. (c) Given a normal distribution with μ = 30 and σ = 6, find the two values of x that             contains the middle 75% of the normal curve area.
Given a standard normal distribution, find the area under the curve which lies (i) to the...
Given a standard normal distribution, find the area under the curve which lies (i) to the left of z = 1.43; (ii) to the right of z = -0.89; (iii) between z = -2.16 and z = -0.65. Given a standard normal distribution, find the value of k such that (i) P(Z < k) = 0.0427 (ii) P(Z > k) = 0.2946 (iii) P(-0.93 < Z < k) = 0.7235
using the unit normal table, find the proportion under the standard normal curve that lies to...
using the unit normal table, find the proportion under the standard normal curve that lies to the right of the following values (round answers to four decimal places): z= -1.35 z= -2.70 using the same table find the proportion under the standard normal curve that lies between the following values (round your answers to four decimal spaces) the mean and z= 1.96 the mean and z=0 z= -1.40 and z=1.40 z= -.90 and z= -.70 z=1.00 and z= 2.00
Using the unit normal table, find the proportion under the standard normal curve that lies to...
Using the unit normal table, find the proportion under the standard normal curve that lies to the right of the following values. (Round your answers to four decimal places.) (a)    z = 2.00 (b)    z = −1.75 (c)    z = −2.20 (d)    z = 0 (e)    z = 1.96
Using the unit normal table, find the proportion under the standard normal curve that lies to...
Using the unit normal table, find the proportion under the standard normal curve that lies to the right of the following values. (Round your answers to four decimal places.) (b) z = −1.05 (c) z = −2.40
Find z such that 85% of the standard normal curve lies to the left of z....
Find z such that 85% of the standard normal curve lies to the left of z. (Round your answer to two decimal places.) z =
Determine the area under the standard normal curve that lies to the left of ​(a) Upper...
Determine the area under the standard normal curve that lies to the left of ​(a) Upper Z equals 0.53 comma ​(b) Upper Z equals 0.24​, ​(c) Upper Z equals 1.08​, and ​(d) Upper Z equals negative 1.39. ​(a) The area to the left of Zequals0.53 is
Determine the area under the standard normal curve that lies to the left of ​(a) Upper...
Determine the area under the standard normal curve that lies to the left of ​(a) Upper Z equals 0.08 commaZ=0.08, ​(b) Upper Z equals 0.51Z=0.51​, ​(c) Upper Z equals negative 1.15Z=−1.15​, and ​(d) Upper Z equals 0.56Z=0.56. ​(a) The area to the left of Zequals=0.080.08 is   nothing. ​(Round to four decimal places as​ needed
Find z such that 5.4% of the standard normal curve lies to the right of z....
Find z such that 5.4% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.) z =   Find the z value such that 83% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.) z =   Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.1 millimeters (mm) and a standard deviation...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT