Use the central limit theorem to find the probability that the sample mean is between two given real numbers - High school Statistics & Probabilities Exercises

Consider a sample with the following characterization:

\mu =582
\sigma = 65
Size: 25

Let m be the sample mean. Use the central limit theorem to determine approximately P\left(564\le m\le 600\right).

P\left(564 \lt m \lt 600\right)= 0.83

P\left(564 \lt m \lt 600\right)= 0.27

P\left(564 \lt m \lt 600\right)= 0.53

P\left(564 \lt m \lt 600\right)=0.57

Consider a sample with the following characterization:

\mu =364
\sigma = 35
Size: 49

Let m be the sample mean. Use the central limit theorem to determine approximately P\left(358\le m\le 370\right).

P\left(358\le m\le 370\right)=0.77

P\left(358\le m\le 370\right)=0.23

P\left(358\le m\le 370\right)=0.45

P\left(358\le m\le 370\right)=0.37

Consider a sample with the following characterization:

\mu =131
\sigma =80
Size: 16

Let m be the sample mean. Use the central limit theorem to determine approximately P\left(100\le m\le 200\right).

P\left(100\le m\le 200\right)=0.94

P\left(100\le m\le 200\right)=0.39

P\left(100\le m\le 200\right)=0.06

P\left(100\le m\le 200\right)=0.45

Consider a sample with the following characterization:

\mu =177
\sigma = 48
Size: 64

Let m be the sample mean. Use the central limit theorem to determine approximately P\left(171\le m\le 189\right).

P\left(171\le m\le 189\right) = 0.82

P\left(171\le m\le 189\right) = 0.28

P\left(171\le m\le 189\right) = 0.45

P\left(171\le m\le 189\right) = 0.57

Consider a sample with the following characterization:

\mu =1\ 216
\sigma = 660
Size: 121

Let m be the sample mean. Use the central limit theorem to determine approximately P\left(1\ 200\le m\le 1\ 300\right).

P\left(1\ 200\le m\le 1\ 300\right)=0.53

P\left(1\ 200\le m\le 1\ 300\right)=0.35

P\left(1\ 200\le m\le 1\ 300\right)=0.66

P\left(1\ 200\le m\le 1\ 300\right)=0.37

Consider a sample with the following characterization:

\mu =43
\sigma =18
Size: 81

Let m be the sample mean. Use the central limit theorem to determine approximately P\left(40\le m\le 45\right).

P\left(40\le m\le 45\right)=0.77

P\left(40\le m\le 45\right)=0.87

P\left(40\le m\le 45\right)=0.53

P\left(40\le m\le 45\right)=0.38

Consider a sample with the following characterization:

\mu =77
\sigma = 66
Size: 36

Let m be the sample mean. Use the central limit theorem to determine approximately P\left(90\le m\le 100\right).

P\left(90\le m\le 100\right)=0.1

P\left(90\le m\le 100\right)=0.92

P\left(90\le m\le 100\right)=0.27

P\left(90\le m\le 100\right)=0.24