The graph below depicts the standard normal distribution with a mean of 0 and st

Question

The graph below depicts the standard normal distribution with a mean of 0 and standard deviation of 1. Find the indicated z-score for the shaded area. The shaded area is 0.7599.

– 1.08 (b) 0.71 (c) 1.08 (d) -0.71 (e) -.70

Assume that weight of newborn babies is normally distributed with a mean of 10 lbs and a standard deviation of 2 lbs.  Find the probability that a randomly selected newborn baby is greater than 7 lbs.

(a) .0668 (b) .9332 (c) -1.5 (d) .1587

9 Assume that men heights are normally distributed with a mean 69.0 inches and a standard deviation of 2.8 inches. In order to join the U.S. Marine Corp, the requirement is that men should have heights between 64 inches and 80 inches. Find the percentage of men who meet the height requirement.

(a) 68% (b) 93% (c) 96% (d) 85%

10 Refer to question 9 above. If the height requirements for the U.S. Marine Corp are changed so that all men are eligible EXCEPT the shortest 2% and the tallest 5%, what are the new height requirements?

(a) 63 - 74 (b) 68 - 84 (c) 67 - 76 (d) 64 - 77

11 Questions 11– 14 pertain to the following: Assume that weight of newborn babies is normally distributed with a mean of 7 lbs and a standard deviation of 2.5 lbs.  Find the probability that a randomly selected newborn baby is greater than 7 lbs.

(a) .2881 (b) .5000 (c) .7881 (d) .2119

12 Refer to question 11 above.  Find the probability that a randomly selected newborn baby is less than 11.5 lbs?

(a) .4641 (b). 0359 (c) .9641 (d) .8641

13 Refer to question 11 above.  What would be the Z-score of a baby whose weight was 7 lbs?

(a) 0 (b) –1.0 (c) 1.0 (d) 0.5

14 Refer to question 11 above.  Find the value of P90.  That is, find the weight separating the bottom 90% of babies from the top 10%.

(a) 3.2 lbs (b) 10.2 lbs (c) 4.8 lbs (d) 7.6 lbs

15 A teacher gives a test and gets normally distributed results with a mean of 50 and a standard deviation of 10.  The letter grade A is assigned only to those in the top 10%.  What score will a student need to receive an A?

(a) > 62.8 (b) > 66.8 (c) > 68.8 (d) > 52.5   

16 Refer to question 15 above.  What percentage of students will have a score between 37 and 76?

(a) .4032 (b) .4953 (c) .8985 (d) .9357

17 Refer to question 15 above.  What percentage of students will have a score of 69 or higher?

(a) .4713 (b) .9713 (c) .0287 (d) .5287

Explanation / Answer

2) mean =10 , s = 2 , x = 7

By normal distribution formula,

z = ( x- mean) / s

= ( 7 - 10) / 2

= -1.5

Now, we need to find p(z > -1.5)

p(x > 7 ) = p( z > -1.5) = 0.9332

3)

mean =69, s = 2.8 , P(x < 64 < 80)

By normal distribution formula,

z = ( x- mean) / s

= p(( 64 - 69) / 2.8 < z < (80 - 69)/ 2.8)

= p( -1.78 < z < 3.92)

Now, we need to find p(z <-1.78 <z <3.92)

p(64 < x < 80 ) = p( -1.78 < z < 3.92) = 0.9629 = 96%

11)

mean =7 , s = 2.5 , x = 7

By normal distribution formula,

z = ( x- mean) / s

= ( 7 - 7) / 2.5

= 0

Now, we need to find p(z >0)

p(x > 7 ) = p( z > 0) = 0.5

12)

mean =7 , s = 2.5 , x = 11.5

By normal distribution formula,

z = ( x- mean) / s

= ( 11.5 - 7) / 2.5

= 1.8

Now, we need to find p(z > 1.8)

p(x > 11.5 ) = p( z > 1.8) = 0.0359

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