# Probability of weight of giant squid being above 750 lbs

#### sweetkendra

##### New member
Okay, I was instructed to start this off by calculating z scores and using the table of which I know how to do, but This problem is still confusing me so much and I have a test in the morning. Any help someone can give me will be greatly appreciated.

The weight of the giant squid is a normally distributed variable with an estimated average of 660 lbs. The standard deviation is estimated to be 62.5 lbs. If a giant squid is selected at random, what is the probability that it weighs more than 750 lbs? What is the probability that it weighs between 500 and 700 lbs? What is the oprobability that it weighs between 700 and 750 lbs? If a random sample of 35 giant squid is selected, what is the probability that the mean weight is greater than 690 lbs? And what is the probability that the mean weight is less than 675 lbs using the 35 giant squid selected???

I know that to do a z score you use the formula of z=value-mean/standard deviation.

#### galactus

##### Super Moderator
Staff member
For the first part, be careful, it says P(x>750). z -scores go from the left. So you subtract from 1.

$$\displaystyle \frac{750-660}{62.5}=1.44$$

Looking that up in the table we get 0.9251. But that is P(x<750). So 1-0.9251=0.0749

See?. Read them careful.

#### wjm11

##### Senior Member
The weight of the giant squid is a normally distributed variable with an estimated average of 660 lbs. The standard deviation is estimated to be 62.5 lbs. If a giant squid is selected at random, what is the probability that it weighs more than 750 lbs? What is the probability that it weighs between 500 and 700 lbs? What is the probability that it weighs between 700 and 750 lbs? If a random sample of 35 giant squid is selected, what is the probability that the mean weight is greater than 690 lbs? And what is the probability that the mean weight is less than 675 lbs using the 35 giant squid selected?
What is the distribution when your sample size is 35? Answer: the sample mean will be the same as the population mean, but the sample std. dev. will be 62.5/(35^.5).