1. The length of human pregnancies from conception to birth varies according to

Question

1. The length of human pregnancies from conception to birth varies according to a distribution that can be modeled by a normal random variable with mean 268 days and standard deviation 15 days.

Question 1. What percent of pregnancies last less than 240 days? Note that the answer is requested as a percent. Use 2 decimal places in your answer. %

Question 2. What percent of pregnancies last between 240 and 270 days? Note that the answer is requested as a percent. Use 2 decimal places in your answer. % Question 3. The longest 20% of pregnancies last at least how many days? (round to the nearest whole day) days.

2. The Nelson Company makes the machines that automatically dispense soft drinks into cups. Many national fast food chains such as McDonald's and Burger King use these machines. A study by the company shows that the actual volume of soft drink that goes into a 16-ounce cup per fill can be approximated by a normal model with mean 16 ounces and standard deviation 0.33 ounces. A new 16-ounce cup that is being considered for use actually holds 16.6 ounces of drink.

Question 1. What is the probability that a new cup will overflow when filled by the automatic dispenser? (Use 4 decimal places)

Question 2. The company wishes to adjust the dispenser so that the probability that a new cup will overflow is .006. At what value should the mean amount dispensed by the machine be set to satisfy this wish? (Use 2 decimal places in your answer and use 0.33 ounces for the standard deviation). ounces.

3. The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of a checking account is defined to be the balance in the checking account at 2:00pm.The bank has found that for all personal checking accounts the mean of all the daily balances is $850 and the standard deviation is $100. In addition, the distribution of personal checking account daily balances can be approximated very well with a normal model.

Question 1. What percentage of the bank's customers carry daily balances between $700 and $1,000?

% (Use 2 decimal places in your answer. Note that the answer is requested as a percent, that is, a value between 0 and 100).

Question 2.The bank is considering paying interest to customers carrying daily checking account balances in excess of a certain amount. If the bank does not want to pay interest to more than 4% of its checking account customers, what is the minimum daily balance on which it should be willing to pay interest? (Round your answer to the nearest dollar)

Explanation / Answer

Ans:

1)Given that

mean=268

standard deviation=15

a)

z(240)=(240-268)/15=-1.867

P(z<-1.867)=0.0310 or 3.10%

b)

z(270)=(270-268)/15=0.133

P(-1.867<z<0.133)=P(z<0.133)-P(z<-1.867)=0.5530-0.0310=0.5220 or 52.20%

2)

a)z=(16.6-16)/0.33=1.82

P(overflow)=P(x>16.6)=P(z>1.82)=0.0344

b)

P(Z>z)=0.006

P(Z<z)=1-0.006=0.994

z=2.512

2.512=(16.6-mean)/0.33

mean=16.6-2.512*0.33=15.77

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