Answer :
Answer:
Step-by-step explanation:
Given that a delivery driver has an average daily gasoline expense of $55.00. The standard deviation is $10.00.
As per central limit theorem, for samples of large size drawn at random, the sample mean follows a normal distribution irrespective of the original distribution.
Hence here we can say sample mean
[tex]\bar X =N(55,\frac{10}{\sqrt{54} } )[/tex]
= N(55,1.361)
required probability =
the probability the mean of his sample will be between $45.00 and $65.00
= [tex]P(45<\bar x<65)\\= F(65)-F(45)\\= 1[/tex]
i.e. almost a certain event.