Thread: Probability w/ standard deviation

hey guys, could use some help and guidance on my stat homework. unfortunately i missed a week of class and my book is almost useless. if anyone can give me some help on these i'd really appreciate it.

"DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. the quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of .3 ounces. assume the contents of the bottles are normally distributed.

a) what percentage of all bottles produced contains more than 6.51 ounces of vitamins?
b) what percentage of all bottles produced contains less than 5.415 ounces of vitamins?
c) what percentage of bottles produced contrains between 5.46 to 6.495 ounces?
d) ninety-five percent of the bottles will contain at least how many ounces?


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The average lifetime of a lightbulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken

a) what are the expected value, standard deviation, and shape of the sampling distribution of x? ---- in the homework the x has a line over it but i dunno how to do that on here
b) what is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours?
c) what is the probability that the average life in the sample will be greater than 3,219.24 hours?
d) what is the probability that the average life in the sample will be less taht 3,180.96 hours?

thank you so much guys, i really appreciate it

The first question says the weight of the vitamins is normally distributed. Therefore use a z-score and normal cdf table to find the answers.

Here is the z-score transformation.

Use this to change your problems into z-scores then find a table to reference, there are hundreds of them on the internet. ou can even use ms-excel to give you an answer for the normdist() function.