Compute the following probabilities: If Y is distributed N(1, 4), find Pr ( Y ≤ 3 ) . If Y is distributed N(3, 9), find Pr ( Y > 0 ) . If Y is distributed N(50, 25), find Pr ( 40 ≤ Y ≤ 52 ) . If Y is distributed N(5, 2), find Pr ( 6 ≤ Y ≤ 8 ) .

a) If Y is distributed N(1, 4), Pr (Y ≤ 3) = 0.84134

b) If Y is distributed N(3, 9), Pr (Y > 0) = 0.84134

c) If Y is distributed N(50, 25), Pr (40 ≤ Y ≤ 52) = 0.63267

d) If Y is distributed N(5, 2), find Pr (6 ≤ Y ≤ 8) = 0.22185

Step-by-step explanation:

With the logical assumption that all of these distributions are normal distribution,

a) Y is distributed N(1, 4), find Pr ( Y ≤ 3 )

Mean = μ = 1

Standard deviation = √(variance) = √4 = 2

To find the required probability, we first standardize 3

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (y - μ)/σ = (3 - 1)/2 = 1

We'll use data from the normal probability table for these probabilities

The required probability

Pr ( Y ≤ 3 ) = P(z ≤ 1) = 0.84134

b) If Y is distributed N(3, 9), find Pr ( Y > 0 )

Mean = μ = 3

Standard deviation = √(variance) = √9 = 3

To find the required probability, we first standardize 0

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (y - μ)/σ = (0 - 3)/3 = -1

We'll use data from the normal probability table for these probabilities

The required probability

Pr ( Y > 0) = P(z > -1) = 1 - P(z ≤ -1) = 1 - 0.15866 = 0.84134

c) If Y is distributed N(50, 25), find Pr (40 ≤ Y ≤ 52).

Mean = μ = 50

Standard deviation = √(variance) = √25 = 5

To find the required probability, we first standardize 40 and 52.

For 40,

z = (y - μ)/σ = (40 - 50)/5 = -2

For 52,

z = (y - μ)/σ = (52 - 50)/5 = 0.4

We'll use data from the normal probability table for these probabilities

The required probability

Pr (40 ≤ Y ≤ 52) = P(-2.00 ≤ z ≤ 0.40)

= P(z ≤ 0.40) - P(z ≤ -2.00)

= 0.65542 - 0.02275

= 0.63267

d) If Y is distributed N(5, 2), find Pr ( 6 ≤ Y ≤ 8 )

Mean = μ = 5

Standard deviation = √(variance) = √2 = 1.414

To find the required probability, we first standardize 6 and 8.

For 6,

z = (y - μ)/σ = (6 - 5)/1.414 = 0.71

For 8,

z = (y - μ)/σ = (8 - 5)/1.414 = 2.12

We'll use data from the normal probability table for these probabilities

The required probability

Pr (6 ≤ Y ≤ 8) = P(0.71 ≤ z ≤ 2.12)

= P(z ≤ 2.12) - P(z ≤ 0.71)

= 0.983 - 0.76115

= 0.22185

Hope this Helps!!

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d

i need a diagram

step-by-step explanation:

no