# Thread: mean and standard deviation

1. ## 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?

2. ## 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).

3. ## 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.

4. ## Re: mean and standard deviation

#2)
mean=470
sd=60
10% fastest = those faster than 393.11 sec

5. ## Re: mean and standard deviation

Soda machine:

mean=12.099 results in on 3% spillage

6. ## Re: mean and standard deviation

Seat belts:

P[x>579|0.7,800] = 0.065349

7. ## 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.

8. ## 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.

9. ## 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.