Let the number of geese be x.
Then number of goats is 22-x.
A goose has 2 legs, and a goat has 4.
There are a total of 82 legs.
So,
2x + 4(22-x) = 82
2x + 88 - 4x = 82
-2x = -6
x = 3
There are 3 geese and (22-3=) 19 goats.
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Let X be the normal variable with mean μ =50 and standard deviation σ =2
We have to find probability that x is between 47 and 54
P(47 < X < 54) = P(X < 54) - P(X < 47)
=
- 
= P(Z < 2) - P(Z < -1.5)
Using standard normal z score table to find probabilities we get
P(Z < 2) = 0.9772
P(Z < -1.5) = 0.0668
P(47 < X < 54) = P(Z < 2) - P(Z < -1.5)
= 0.9772 - 0.0668
P(47 < X < 54) = 0.9104
The probability that x is between 47 and 54 is 0.9104
The decimal is about 1.1 and you can’t simplify it