# mean and standard deviation

• Oct 13th 2012, 07:59 AM
silver163
mean and standard deviation
I got two problems that are statistics.

#1

Find a value of the standard normal random variable z, called Z0 such that P(-Z0 ≤ Z ≤ Z0) = 0.98

#2

The time for the event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 60 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?

• Oct 13th 2012, 04:57 PM
chiro
Re: mean and standard deviation
Hey silver163.

Looking at 1) first, do you know how to use tables or computer software to do this? (You won't be able to do it by hand effectively).
• Oct 13th 2012, 07:32 PM
silver163
Re: mean and standard deviation
i figured out the first one but i cannot figure out the second one. but to answer your question i know how to use tables.

the amount of soda a dispensing machine pours into 12-ounce can of soda follows a normal distribution with a standard deviation of 0.16 ounce. Every can that has more than 12.40 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that must be cleaned because of spillage to 3%?

Transportation officials tell us that 70% of drivers wear seat belts while driving. Find the probability that more than 579 drivers in a sample of 800 drivers wear seat belts.
• Oct 13th 2012, 09:11 PM
MaxJasper
Re: mean and standard deviation
#2)
mean=470
sd=60
10% fastest = those faster than 393.11 sec
• Oct 13th 2012, 09:19 PM
MaxJasper
Re: mean and standard deviation
Soda machine:

mean=12.099 results in on 3% spillage
• Oct 13th 2012, 09:21 PM
MaxJasper
Re: mean and standard deviation
Seat belts:

P[x>579|0.7,800] = 0.065349
• Oct 14th 2012, 12:07 PM
silver163
Re: mean and standard deviation
Thanks MaxJasper! I appreciate it greatly. But can you please tell me how you solved it? That's very important to me.
• Oct 14th 2012, 12:47 PM
MaxJasper
Re: mean and standard deviation
1st two problems find z from Normal dist tables then estimate other parameters.

3rd problem use Normal dist approximation to Binomial dist by:
mean=n*p
q=1-p
sd=sqrt(n*p*q)
and again use tables of Normal dist.
• Oct 14th 2012, 02:05 PM
silver163
Re: mean and standard deviation
thanks MaxJasper but can you give me more details? i am particularly having difficulty when percentages and values are involved.
• Oct 14th 2012, 04:45 PM
silver163
Re: mean and standard deviation