30 ATM Withdrawals According to Crown ATM Network the mean A

30. ATM Withdrawals According to Crown ATM Network, the mean ATM withdrawal is $67. Assume that the standard deviation for withdrawals is $35. (a) Do you think the variable \'\'ATM withdrawal\'\' is normally distributed? If not, what shape would you expect the variable to have? (b) If a random sample of 50 ATM withdrawals is obtained, describe the sampling distribution of x, the mean withdrawal amount. (c) Determine the probability of obtaining a sample mean withdrawal amount between $70 and $75.

Solution

mean=67

sd=35

a.)No, the variable %u201CATM withdrawal%u201D is not

likely normally distributed. It is likely

skewed right.

b.)Because the sample is large, n = 50 > 30,

the sampling distribution of x is

approximately normal with mean=67

sd=35/sqrt(50)=4.949

c.)P(70<X<75)=P(70-67/4.95<Z<75-67/4.95)=P(0.61<Z<1.62)=0.9474-0.7291=0.2183