Question

Consider the following. (Give your answers correct to two decimal places.)

(a) Find the standard score (*z*) such that the area
below the mean and above *z* under the normal curve is
0.3961.

(b) Find the standard score (*z*) such that the area below
the mean and above *z* under the normal curve is
0.4812.

(c) Find the standard score (*z*) such that the area below
the mean and above *z* under the normal curve is 0.3733.

Answer #1

a) We are to find k here such that:

P( k < Z < 0) = 0.3961 because 0 is the mean for the standard
normal variable.

Now, as we know that P(Z < 0) = 0.5, because the distribution
is symmetric about mean, therefore

P(Z < k) = 0.5 - P( k < Z < 0) = 0.5 - 0.3961 = 0.1039

From standard normal tables, we have:

P(Z < -1.260) = 0.1039

**Therefore -1.26 is the required test statistic value
here.**

b) Again using the same methodology as above,

P(Z < k) = P(Z < 0.5) - P(k < Z < 0.5) = 0.5 - 0.4812 =
0.0188

From standard normal tables, we have:

P(Z < -2.08) = 0.0188

**Therefore -2.08 is the required z value
here.**

c) Again using the same methodology as above,

P(Z < k) = P(Z < 0.5) - P(k < Z < 0.5) = 0.5 - 0.3733 =
0.1267

From standard normal tables, we have:

P(Z < -1.14) = 0.1267

**Therefore -1.14 is the required z value
here.**

Consider the following. (Give your answers correct to two
decimal places.) (a) Find z(0.1). (b) Find z(0.26). (c) Find
z(0.7). (d) Find z(0.92).
You may need to use the appropriate table in Appendix B to
answer this question.

Assume a normal distribution. (Give your answer correct to two
decimal places.)
(a) Find the z-score associated with the 59th percentile.
(b) Find the z-score associated with the 82nd percentile.
(c) Find the z-score associated with the 92nd percentile.

Consider the following. (Give your answers correct to four
decimal places.)
(a) Find P(-2 < z < 0.00).
(b) Find P(-1.87 < z < 2.07).
(c) Find P(z < -1.44).
(d) Find P(z < -0.45).
(e) Find P(-3.1 < z < 0.00).
(f) Find P(-2.41 < z < 1.34).
(g) Find P(z < -2.23).
(h) Find P(z > 2.34).

a)Find the area under the standard normal curve between
z = -1.86 and z = 1.1, P(-1.86 <
z < 1.1). (Give your answer correct to four decimal
places.)
b)Find the area under the standard normal curve between
z = -2.53 and z = 1.4, P(-2.53 <
z < 1.4). (Give your answer correct to four decimal
places.)
c)Consider the normal curve. (Give your answers correct to four
decimal places.)
1) Find the area to the right of z =...

Compute the area under the standard normal curve. Round your
answers to four decimal places. (a) The area to the right of z =
1.81 equals
(b) The area to the left of z = − 1.5 equals
(c) The area between z = 0 and z = 3.33 equals
PLEASE SHOW WORK

Find the area under the standard normal curve that lies between
the following two z values. Round your answers to at least four
decimal places.
(a)Find the area under the standard normal curve that lies
between = z − 1.28 and = z 1.36 .
(b)Find the area under the standard normal curve that lies
between = z − 2.17 and = z − 1.92 .
(c)Find the area under the standard normal curve that lies
between = z 1.36...

Consider the following hypothesis-testing situations. (Give your
answers correct to four decimal places.)
(a) Determine the p-value for Ho:
p = 0.5, Ha: p ≠ 0.5,
z = 1.59.
(b) Determine the p-value for Ho:
p = 0.7, Ha: p ≠ 0.7,
z = -2.32.
(c) Determine the p-value for Ho:
p = 0.4, Ha: p > 0.4,
z = 1.02.
(d) Determine the p-value for Ho:
p = 0.2, Ha: p < 0.2,
z = -1.5.

Consider the following hypothesis-testing situations. (Give your
answers correct to four decimal places.)
(a) Determine the p-value for Ho:
p = 0.5, Ha: p ≠ 0.5,
z = 1.4.
(b) Determine the p-value for Ho:
p = 0.7, Ha: p ≠ 0.7,
z = -2.35.
(c) Determine the p-value for Ho:
p = 0.4, Ha: p > 0.4,
z = 0.94.
(d) Determine the p-value for Ho:
p = 0.2, Ha: p < 0.2,
z = -1.5.

Using the TI 84 calculator, find the area under the standard
normal curve. Round the answers to four decimal places.
a) find the area under the standard normal curve to the left of
z= -2.16
b) find the area under the standard normal curve to the right of
z =-0.04
c) find the area under the standard normal curve that lies
between z =-2.3 and z=1.08
d) find the area under the standard normal curve that lies
outside the interval...

5. Consider the following hypothesis-testing situations. (Give
your answers correct to four decimal places.)
(a) Determine the p-value for Ho:
p = 0.5, Ha: p â‰ 0.5,
z = 1.4.
(b) Determine the p-value for Ho:
p = 0.7, Ha: p â‰ 0.7,
z = -2.31.
(c) Determine the p-value for Ho:
p = 0.4, Ha: p > 0.4,
z = 1.03.
(d) Determine the p-value for Ho:
p = 0.2, Ha: p < 0.2,
z = -1.67.

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