Norm Dist and Sampling

Question 3

For Z ~ N(0, 1), find P(Z > -0.78).

Answer 3

0.7823

Question 4

For X ~ N(60, 91), find P(X > 72.0).

Answer 4

0.1042

Question 5

For X ~ N(70, 69), find P(X < 58.0).

Answer 5

0.0743

Question 6

For Z ~ N(0, 1), find P(Z > -2.22).

Answer 6

0.9868

Question 7

For X ~ N(60, 147), find P(X < 52).

Answer 7

0.2547

Question 8

Find z if P(Z < z) = 0.95.

Answer 8

1.6449

Question 9

For X ~ N(70, 114), find P(X < 62).

Answer 9

0.2268

Question 10

Approximate P(X ≥ 21) for X ~ Bin(n=50, p=0.5) using normal approximation with continuity correction.

Answer 10

0.8985

Question 11

Find z if P(Z < z) = 0.95.

Answer 11

1.6449

Question 12

Find z if P(Z < z) = 0.975.

Answer 12

1.96

Question 13

For X ~ N(70, 33), find P(X < 62.5).

Answer 13

0.0958

Question 14

For Z ~ N(0, 1), find P(Z > 2.2).

Answer 14

0.0139

Question 15

For X ~ N(50, 99), find P(X < 40).

Answer 15

0.1574

Question 16

For X ~ N(100, 146), find P(X < 90).

Answer 16

0.2039

Question 17

For X ~ N(60, 101), find P(50 < X < 70).

Answer 17

0.6803

Question 18

For X ~ N(50, 81), find P(X < 35.0).

Answer 18

0.0478

Question 19

For Z ~ N(0, 1), find P(Z < 0.38).

Answer 19

0.648

Question 20

For Z ~ N(0, 1), find P(Z > -0.95).

Answer 20

0.8289

Question 21

For X ~ N(70, 116), find P(X < 60).

Answer 21

0.1766

Question 22

Find z if P(Z < z) = 0.9.

Answer 22

1.2816

Question 23

For X ~ N(100, 34), find P(96.0 < X < 104.0).

Answer 23

0.5073

Question 24

Approximate P(X ≥ 28) for X ~ Bin(n=50, p=0.5) using normal approximation with continuity correction.

Answer 24

0.2398

Question 25

Approximate P(X ≥ 23) for X ~ Bin(n=50, p=0.4) using normal approximation with continuity correction.

Answer 25

0.2352

Question 26

For X ~ N(50, 39), find P(42 < X < 58).

Answer 26

0.7998

Question 27

For Z ~ N(0, 1), find P(Z > -0.19).

Answer 27

0.5753

Question 28

For X ~ N(100, 72), find P(97.5 < X < 102.5).

Answer 28

0.2317

Question 29

For X ~ N(100, 134), find P(X > 120).

Answer 29

0.042

Question 30

For Z ~ N(0, 1), find P(Z > 1.83).

Answer 30

0.0336

Question 31

For X ~ N(60, 46), find P(57.5 < X < 65).

Answer 31

0.4133

Question 32

For X ~ N(70, 45), find P(X > 80).

Answer 32

0.068

Question 33

Give the 95% confidence interval for p̂ = 0.5, n = 100.

Answer 33

(0.402, 0.598)

Question 34

Find required sample size for margin of error 0.04 at 95% confidence, p = 0.5.

Answer 34

0

Question 35

Compute the Standard error for p = 0.6, n = 80.

Answer 35

0.0548

Question 36

Give the 95% confidence interval for p̂ = 0.55, n = 100.

Answer 36

(0.4525, 0.6475)

Question 37

Compute the Standard error for p = 0.5, n = 100.

Answer 37

0.05

Question 38

Interpret: A 95% confidence interval for p is (0.48, 0.52). Does it guarantee p is in the interval?

Answer 38

No

Question 39

Find the margin of error for p = 0.5, n = 100, 95% confidence.

Answer 39

0.098

Question 40

Find required sample size for margin of error 0.04 at 95% confidence, p = 0.5.

Answer 40

0

Question 41

Interpret: A 95% confidence interval for p is (0.48, 0.52). Does it guarantee p is in the interval?

Answer 41

No

Question 42

Find the margin of error for p = 0.5, n = 100, 95% confidence.

Answer 42

0.098

Question 43

Compute the Standard error for p = 0.5, n = 80.

Answer 43

0.0559

Question 44

Give the 95% confidence interval for p̂ = 0.55, n = 120.

Answer 44

(0.461, 0.639)

Question 45

Compute the Standard error for p = 0.6, n = 100.

Answer 45

0.049

Question 46

Find the margin of error for p = 0.4, n = 150, 95% confidence.

Answer 46

0.0784

Question 47

Find the margin of error for p = 0.4, n = 100, 95% confidence.

Answer 47

0.096

Question 48

Interpret: A 95% confidence interval for p is (0.48, 0.52). Does it guarantee p is in the interval?

Answer 48

No

Question 49

Find required sample size for margin of error 0.05 at 95% confidence, p = 0.5.

Answer 49

0

Question 50

Find the margin of error for p = 0.5, n = 100, 95% confidence.

Answer 50

0.098

Question 51

Give the 95% confidence interval for p̂ = 0.45, n = 120.

Answer 51

(0.361, 0.539)

Question 52

Interpret: A 95% confidence interval for p is (0.48, 0.52). Does it guarantee p is in the interval?

Answer 52

No