Answer:
A)what is the probability that the sample mean will be More than 58 pounds
P(x>58)
Formula :
Substitute the values :
refer the z table
P(x<58)=0.5359
P(X>58)=1-P(x<58)=1-0.5359=0.4641
Hence the probability that the sample mean will be More than 58 pounds is 0.4641
B)what is the probability that the sample mean will be More than 57 pounds
P(x>57)
Formula :
Substitute the values :
refer the z table
P(x<57)=0.5040
P(X>57)=1-P(x<57)=1-0.5040=0.496
Hence the probability that the sample mean will be More than 57 pounds is 0.496
C)what is the probability that the sample mean will be Between 55 and 57 pound
Formula :
Substitute the values :
refer the z table
P(x<57)=0.5040
Formula :
Substitute the values :
refer the z table
P(x<55)=0.4443
P(55<x<57)=P9x<57)-P(x<55) =0.5040-0.4443=0.0597
Hence the probability that the sample mean will be Between 55 and 57 pounds is 0.0597
D)what is the probability that the sample mean will be Less than 53 pounds
Formula :
Substitute the values :
refer the z table
P(x<53)=0.3783
The probability that the sample mean will be Less than 53 pounds is 0.3783
E)what is the probability that the sample mean will be Less than 48 pounds
Formula :
Substitute the values :
refer the z table
P(x<48)=0.2358
The probability that the sample mean will be Less than 48 pounds is 0.2358