Biostatistics Quiz Normal Distribution Please do not write on this sheet. Use La

Question

Biostatistics Quiz Normal Distribution Please do not write on this sheet. Use Lane's normal and inverse normal calculators to obtain answers to the following questions. While performing calculations, keep as many decimals as the calculators will allow (do this by using the online Google calculator, then copy-paste numbers into Lane's calculators). Do not round off your final answers, Just report what Lane's calculators give you 1. If scores are normally distributed with a mean of 36 and a standard deviation of 9, what percent of the scores is between 24 and 45? What proportion of a normal distribution is within 1.5 standard deviations of the mean? A test has a mean of 55 and variance of 36. What score would a student need to be in the top 30%? A normal distribution has a mean of 20 and a standard deviation of 5, find a Z score for 19. On a stretch of 1-95, the current speed limit is 55 mph. However, most drivers have an average speed of 76 mph with standard deviation of 10 mph. A new speed limit will be put in place so that only 15% of drivers are actually speeding. What is this new speed limit? A variable has a mean of 140 and standard deviation of 10. One score is randomly sampled. What is the probability that the score will be above 170? Use the normal approximation of the binomial to find the probability of getting between 12 to 17 heads in 26 flips of a coin. In a population of butterflies, 25% are monarchs. we count 35 monarchs out of 100 butterflies visiting flowers. We want to know the probability of 35 or more monarchs visiting the flowers given that this number is higher than the percentage of monarchs in the population. a. Can a normal approximation of the binomial be used to solve this problem? Why or why 2. 3. 4. 5. 6. 7. 8. not? Using the normal approximation of the binomial, what is the probability of 35 or more monarchs visiting the flower? Using the binomial calculator, what is the probability of 35 or more monarchs visiting the flower? b. c.

Explanation / Answer

Ans:

5)Given that

mean=76

standard deviation=10

only 15% speeding means that

P(Z>=z)=0.15

P(Z<=z)=1-0.15=0.85

z=NORMSINV(0.85)=1.0364

z=1.0364=(x-76)/10

x-76=10.364

x=86.364

So,new speed limit should be 86.364

6)z=(170-140)/10=30/10=3

P(z>3)=1-P(z<=3)=1-NORMSDIST(3)=1-0.9987=0.0013

7)n=26,p=0.5

mean=np=26*0.5=13

standard deviation=sqrt(np(1-p))=sqrt(13*0.5)=2.55

z(12)=(12-13)/2.55=-0.392

z(17)=(17-13)/2.55=1.569

P(-0.392<=z<=1.569)=NORMSDIST(1.569)-NORMSDIST(-0.392)=0.5941

8)a)yes,we can use normal approximation as np=100*0.25=25>=10

b)mean=25

std dev=sqrt(25*0.75)=4.33

z=(35-25)/4.33=2.31

P(z>=2.31)=1-P(z<2.31)==1-NORMSDIST(2.31)=1-0.9896=0.0104

c)P(k>=35)=1-BINOMDIST(34,100,0.25,TRUE)=1-0.9836=0.0164

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