Normal Distribution - Assessment 1. In a standard normal distribution the mean i

Question

Normal Distribution - Assessment 1. In a standard normal distribution the mean i sand the standard deviation is a) -1,0 b) 0,-1 c) 0,1 d) 1,0 2. What is the area under the standard normal curve corresponding to Z >2.85? a) 0.0022 b) 0.4978 c) 0.9978 d) 0.6103 3. The probability that a standard normal random variable, Z is between -0.90 and 1.60 is a) 0.2389 b) 0.6106 c) 0.7611 d) 1 4. Which is the following about the normal distribution is not true? a) b) c) d) Theoretically, the mean, median and mode are the same. About 68% of the observations fall within one standard deviation from the mean. It is a discrete probability distribution. its parameters are and . 5. The probability that a standard normal random variable, Z is between -2.00 and-0.44 is 6. The probability that a standard normal random variable, Z is below 1.96 is

Explanation / Answer

1)In a standard normal distribution the mean is 0 and standard deviation is 1.

2a) The area under standard normal curve corresponding to Z>2.85 is 0.0022

3c) The probability that a standard normal random variable, Z is between -0.9 and 1.60 is 0.7611.

4c) It is discrete probability distribution.

5) The probability that a standard normal random variable, Z is between -2 and -0.44 is 0.3072

6)The probability that a standard normal random variable, Z is below 1.96 is 0.975

7)

Since =90 and =15 we have:

P ( X<105 )=P ( X<10590 )=P (X<1059015)

Since x=Z and 1059015=1 we have:

P (X<105)=P (Z<1)

By using the standard normal table to conclude that:

P (Z<1)=0.8413

8)Since =62 and =11 we have:

P ( X>51 )=P ( X>5162 )=P ( X>516211)

Since Z=x and 516211=1 we have:

P ( X>51 )=P ( Z>1 )

By using the standard normal table to conclude that:

P (Z>1)=0.8413

Note: I used hit and trial method , so by that I got option A so 51 is lowest mark that Student can have and awarded A.

9) Z score corresponding to this given value is 1.418653

10) area to the left= 1-0.35= 0.65 Z score corresponding to this is0.38532.

Please Note : Post question 11 again.

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