Normal Distribution
Q1. According to the 2007 American Time Use Survey by the Bureau of Q4. The amount of money spent every month on mobile is an important
Labor Statistics, employed adults living in households with no children variable for the marketers. The data was collected and it was found
younger than 18 years engaged in leisure activities for 4.4 hours a day that the population average is 2700 Rs. The population standard
on average. Assume that currently such times are (approximately) deviation was found to be 500 Rs. Compute the following
normally distributed with a mean of 4.4 hours per day and a standard A. Probability of randomly selected person to be spending more
deviation of 1.08 hours per day. Find the probability that the amount of than 1750 Rs.
time spent on leisure activities per day for a randomly chosen B. Probability of randomly selected person to be spending less
individual from the population of interest (employed adults living in
than 3980 Rs.
households with no children younger than 18 years) is:
C. Between 1600 Rs and 3800 Rs.
A. Between 3 and 5 hours per day
B. Less than 2 hours per day D. What is the minimum amount spent by the highest 25%
C. Between 2.2 and 5.6 hours per day customers?
And Calculate. E. What is the maximum amount spent by the lowest 20%
D. What is the highest value of lowest 20%? customers?
E. What is the lowest value of highest 25%? F. What is the maximum and minimum amount spent by the
middle 20% customers?
Q2. The Bank of Connecticut issues Visa and MasterCard credit cards: It is
estimated that the balances on all Visa credit cards issued by the Bank Q5. Stress is a big killer for the drivers. Safe Drive is an organization which
of Connecticut have a mean of $845 and a standard deviation of $270. has embarked upon a study to measure the stress level of those
Assume that the balances on all these Visa cards follow a normal drivers having accidents regularly. (Regularly means at least one
distribution. accident in a month). Mean amount of stress was found to be 84
A. What is the probability that a randomly selected Visa card issued (Maximum of the scale is 120) with a standard deviation of 8, find the
by this bank has a balance between $1000 and $1440? probability that a randomly selected accident prone driver will be
B. What percentage of the Visa cards issued by this bank has a having stress level:
balance of $730 or more? A. Less than 69
C. What is the percentage of the Visa cards issued by this bank has a B. More than 93
balance more than $800? C. Between 75 and 98
D. What is the highest value of balance of lowest 10% of the card D. What is the minimum amount of the stress for the highest 20%
users? stressed?
E. What are the highest and lowest values of balances for the middle E. What is the maximum amount of the stress for the lowest 15%
20% of the users? stressed?
F. What is the maximum and minimum stress level for the middle
Q3. The number of bottles of shampoo sold monthly by a certain discount 60% stressed?
drugstore is a normal random variable with mean 212 and standard
deviation 40. Find the probability that next month’s shampoo sales Q6. Amount of money spent on smoking is on rise at the campus. The
will be: mean amount spent by the students per week is 220 Rs with a
A. Greater than 200 standard deviation of 40 Rs. If a student is randomly picked what is the
B. Less than 250 probability that he will be spending:
C. Greater than 200 but less than 250 A. More than 295 Rs
D. What will be the highest number of shampoos sold for the next B. Between 220 and 285 Rs
month if is in the lowest 25% sales? C. Less than 303 Rs.
E. What will be the highest number of shampoos sold for the next D. What is the minimum amount spent by highest 10% smokers?
month if is in the lowest 25% sales? E. What is the maximum amount spent by the lowest 15%
smokers?
F. What is the maximum and minimum amount spent by the
middle 40% smokers?
