draw the corresponding normal curve Given : Mean = μμ = 425 Standard deviation = σσ = 50 1. P (x > 382.50) = 1 - P (x ≤≤ 382.50) z = x − μσx - μσ = 382.50 − 42550= −42.550=− 0.85= 382.50 - 42550= -42.550=- 0.85 P (z < -0.85) = 0.1977 P (x ≤≤ 382.50) = 0.1977 P (x > 382.50) = 1 - P (x ≤≤ 382.50) = 1 - 0.1977 = 0.8023 2. P (475 < x < 535) = P (x <535 ) - P (x < 475) consider, P (x < 535) z = x − μσx - μσ = 535 − 42550= 11050= 2.2= 535 - 42550= 11050= 2.2 P (z < 2.2) = 0.9861 P (x < 535) = 0.9861 Now, P (x < 475) z = x − μσx - μσ = 475 − 42550= 5050= 1= 475 - 42550= 5050= 1 P (z < 1) = 0.8413 P (x < 475) = 0.8413 As , P (475 < x < 535) = P (x <535 ) - P (x < 475) = 0.9861 - 0.8413 = 0.1448 c) P (x < 404) z = x − μσx - μσ = 404 − 42550= −2150=− 0.42= 404 - 42550= -2150=- 0.42 P (z < -0.42) = 0.3372 P (x < 404) = 0.337
draw the corresponding normal curve
Given :
Standard deviation = σσ = 50
1.
P (x > 382.50) = 1 - P (x ≤≤ 382.50)
z = x − μσx - μσ
= 382.50 − 42550= −42.550=− 0.85= 382.50 - 42550= -42.550=- 0.85
P (z < -0.85) = 0.1977
P (x ≤≤ 382.50) = 0.1977
P (x > 382.50) = 1 - P (x ≤≤ 382.50)
= 1 - 0.1977
= 0.8023
2.
P (475 < x < 535) = P (x <535 ) - P (x < 475)
consider,
P (x < 535)
z = x − μσx - μσ
= 535 − 42550= 11050= 2.2= 535 - 42550= 11050= 2.2
P (z < 2.2) = 0.9861
P (x < 535) = 0.9861
Now,
P (x < 475)
z = x − μσx - μσ
= 475 − 42550= 5050= 1= 475 - 42550= 5050= 1
P (z < 1) = 0.8413
P (x < 475) = 0.8413
As , P (475 < x < 535) = P (x <535 ) - P (x < 475)
= 0.9861 - 0.8413
= 0.1448
c)
P (x < 404)
z = x − μσx - μσ
= 404 − 42550= −2150=− 0.42= 404 - 42550= -2150=- 0.42
P (z < -0.42) = 0.3372
P (x < 404) = 0.3372
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