Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean Complete parts (a) and (b) below. 212 days and standard deviation o 19 days (a) What is the probability that a random sample of 18 pregnancies has a mean gestation period of 206 days or less? needed) The probability that the mean of a random sample of 18 pregnancies is less than 206 days is approximately (Round to four decimal places as needed) (b) What is the probability that a random sample of 56 pregnancies has a mean gestation period of 206 days or less? The probability that the mean of a random sample of 56 pregnancies is less than 206 days is approximately (Round to four decimal places as needed)

Answer 1

Part A:

X ~ N ( µ = 212 , σ = 19 )
P ( X < 206 )
Standardizing the value
Z = ( X - µ ) / (σ/√(n)
Z = ( 206 - 212 ) / ( 19 / √18 )
Z = -1.3398
P ( ( X - µ ) / ( σ/√(n)) < ( 206 - 212 ) / ( 19 / √(18) )
P ( X < 206 ) = P ( Z < -1.34 )
P ( X̅ < 206 ) = 0.0902

Part B

X ~ N ( µ = 212 , σ = 19 )
P ( X < 206 )
Standardizing the value
Z = ( X - µ ) / (σ/√(n)
Z = ( 206 - 212 ) / ( 19 / √56 )
Z = -2.3632
P ( ( X - µ ) / ( σ/√(n)) < ( 206 - 212 ) / ( 19 / √(56) )
P ( X < 206 ) = P ( Z < -2.36 )
P ( X̅ < 206 ) = 0.0091