1 a normal density curve or distribution has which of the...

1. A Normal density curve (or distribution) has which of the following properties? A. It has a peak centered above its mean B. It is skewed C. The standard deviation is always equal to one D. All of the above 2. Assume X is a normally distributed random variable with a known population mean of 240 and a known population standard deviation 30. What can we conclude? A. Approximately 99.7% of the values of X are between 150 and 330. B. Approximately 99.7% of the values of X are between 210 and 270. C. Approximately 99.7% of the values of X are between 180 and 300. D. Approximately 95% of the values of X are between 150 and 330. 3. Scores on the national Pharmacy D. certification exam are approximately normally distributed with a mean of 575 points and a standard deviation of 42 points. If one person is selected at random, what is the probability that person will have score less than 600 points? A. 0.6000 B. 0.2743 C. 0.7257 D. 0.9583

Transcript

00:01 So our first question is telling us to detect the right or wrong sentence out of the following options.

00:06 So the question says a normal density curve has which of the following properties.

00:10 Please note there's a difference between a normal curve and a standard normal distribution curve.

00:17 For a normal curve we have that x is approximately n.

00:20 We have mu, we have sigma.

00:22 And for a standard normal curve we have x is approximately n.

00:26 We have zero.

00:27 We have one.

00:28 This simply implies that for a normal curve.

00:30 It can take any value of mule it can also take any value of zigma but for a standard normal curve the population mule the population mean must always be cost to zero and the standard division was always because to one so let's go back to our question so the first question says it has it has a peak centered about it mean yes for any normal curve the mean is actually the center and the peak centers around the mid so the first option is actually true so let's go to the second option so the second option states that it is cute never a normal distribution either standard normal distribution or a normal distribution it is actually symmetric meaning one half can mirror the other half so our option two is actually false so option three option three say that the standard division is always equals to one this property is the property of a standard normal distribution curve and not a normal distribution curve so option c which is the option is actually wrong too so that's false and the fourth option it states that all of the above so the only right answer in this option is option a so option a is the only right answer there so the second question states that assume s is normally distributed uh assume x is a normally distributed random variable with a known population mean of 240 and a known standard division of 30 what can we conclude so our population mean is 240 so that means our mu is equal to 240 and our sigma is equal to 30 so the first thing first is for us to try to sketch our normal distribution around this value so we have something of this nature so we have the horizontal line so we have our sketch exactly so 240 should be in the middle so 240 plus 30 that gives us 270 plus 30 that gives us 300 and 300 plus 30 that gives us 330 so towards the left we have 240 minus 30 that gives us 210 210 so that gives us 180 and 180 minus 30 that gives us 150 so the first question says um what can we conclude a approximately 99 .7 percent of the values are so before we solve this question, we are going to be using the 98%, the so the 68 % in fact we are going to use, so before we able to answer the question that comes with us using this parameter, we'll be making it of the empirical rule...

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