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Answer:
1. P(X > 305) = $0.1038
2. P ( X > 295) = $0.8962
3. P ( X > 290) = $0.0057
4. P(302 < X < 304 ) = $0.1488
Explanation:
Solution:
Data Given:
Mean = u = $300
SD = Standard Deviation = $56
Sample Size = n = 200
uX = u = 300
SDX = =
= 3.96
1.
P(X > 305) = 1-P ()
P(X > 305) = 1-P (Z < 1.26)
Using Standard Normal Table, we have:
P(X > 305) = 1 - 0.8962
Probability = $0.1038
2.
P ( X > 295) = 1 - P ( )
P ( X > 295) = 1 - P (Z< 1.26)
Using standard normal table, we have:
P ( X > 295) = 1 - 0.1038
P ( X > 295) = $0.8962
3.
P ( X > 290) = P ( )
P ( X > 290) = P ( z< -2.53)
Using Standard normal table, we have:
P ( X > 290) = $0.0057
4.
P(302 < X < 304 ) = P ( )
P(302 < X < 304 ) = P ( 0.51 < z < 1.01)
P(302 < X < 304 ) = P (z < 1.01) - P (z < 0.51)
P(302 < X < 304 ) = 0.8438 - 0.6950
P(302 < X < 304 ) = $0.1488