Question

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).

Answer #1

(a) P(-2<Z<0.00)=P(Z>-2)-P(Z>0)

=1-P(Z<-2)-P(Z>0)

=1-P(Z>2)-P(Z>0) , Due to symmetry

=1-0.022750-0.5

=0.4773

(b) P(-1.87<Z<2.07)=P(Z>-1.87)-P(Z>2.07)

=1-P(Z<-1.87)-P(Z>2.07)

=1-P(Z>1.87)-P(Z>2.07) ; Due to symmetry

=1-0.030742-0.019226

=0.9500

(c) P(Z<-1.44)=P(Z>1.44) Due to symmetry

=0.0749

(d)P(Z<-0.45)=P(Z>0.45) ; Due to symmetry

=0.3264

(e) P(-3.1<Z<0)=P(Z>-3.1)-P(Z>0)

=1-P(Z<-3.1)-P(Z>0)

=1-P(Z>3.1)-P(Z>0) ; Due to symmetry

=1-0.00096760-0.5

=0.4990

(f) P(-2.41<Z<1.34)=P(Z>-2.41)-P(Z>1.34)

=1-P(Z<-2.41)-P(Z>1.34)

=1-P(Z>2.41)-P(Z>1.34)

=1-0.0081975-0.090123

=0.9017

(g) P(Z<-2.23)=P(Z>2.23) ; Due to symmetry

=0.0129

(h) P(Z>2.34)=0.0964

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.

Find the following probabilities. (Round your answers to four
decimal places.)
(a) p(0 < z < 1.62)
(b) p(1.40 < z < 1.83)
(c) p(−0.38 < z < 1.55)
(d) p(z < −1.91)
(e) p(−1.32 < z < −0.86)
(f) p(z < 1.27)

Find the following probabilities. (Round your answers to four
decimal places.)
(a) p(0 < z < 1.42)
(b) p(1.02 < z < 1.65)
(c) p(−0.88 < z < 1.72)
(d) p(z < −2.09)
(e) p(−2.35 < z < −1.19)
(f) p(z < 1.51)

Find the following probabilities. (Round your answers to four
decimal places.)
(a) p(0 < z <
1.45)
(b) p(1.03 < z <
1.65)
(c) p(−0.87 < z <
1.72)
(d) p(z < −2.08)
(e) p(−2.31 < z <
−1.17)
(f) p(z < 1.52)

Find the following probabilities. (Round your answers to four
decimal places.)
(a) p(0 < z <
1.63)
(b) p(1.30 < z <
1.86)
(c) p(−0.37 < z <
1.59)
(d) p(z < −1.93)
(e) p(−1.33 < z <
−0.86)
(f) p(z < 1.25)

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.

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.

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.

Calculate the following probabilities using the standard normal
distribution. (Round your answers to four decimal places.)
(a)
P(0.0 ≤ Z ≤ 1.6)
(b)
P(−0.1 ≤ Z ≤ 0.0)
(c)
P(0.0 ≤ Z ≤ 1.49)
(d)
P(0.6 ≤ Z ≤ 1.51)
(e)
P(−2.05 ≤ Z ≤ −1.76)
(f)
P(−0.02 ≤ Z ≤ 3.54)
(g)
P(Z ≥ 2.60)
(h)
P(Z ≤ 1.66)
(i)
P(Z ≥ 6)
(j)
P(Z ≥ −8)

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