1 Find the standard score z shown on each of the following d

1. Find the standard score (z) shown on each of the following diagrams. (Use Appendix B as necessary.)

2. IQ scores in a certain population are normally distributed with a mean of 99 and a standard deviation of 14. (Give your answers correct to four decimal places.)

(a) Find the probability that a randomly selected person will have an IQ score between 90 and 104

(b) Find the probability that a randomly selected person will have an IQ score above 88.

3. Find the area under the standard normal curve between z = -1.89 and z = 1.25, P(-1.89 < z < 1.25). (Give your answer correct to four decimal places.)   

4.Find the area under the standard normal curve between z = -2.57 and z = 1.55, P(-2.57 < z < 1.55). (Give your answer correct to four decimal places.)

5. Find the area under the standard normal curve between z = -2.79 and z = -1.2, P(-2.79 < z < -1.2). (Give your answer correct to four decimal places.)

6.Find the area under the standard normal curve between z = 0.75 and z = 2.18, P(0.75 < z < 2.18). (Give your answer correct to four decimal places.)

7.The weights of ripe watermelons grown at Mr. Smith\'s farm are normally distributed with a standard deviation of 2.2 lb. Find the mean weight of Mr. Smith\'s ripe watermelons if only 6% weigh less than 16 lb. (Give your answer correct to one decimal place.)

8.The 70-year long-term record for weather shows that for New York State, the annual precipitation has a mean of 39.09 inches and a standard deviation of 4.25 inches. The annual precipitation amount has a normal distribution. (Give your answers correct to four decimal places.)

(a) What is the probability that next year the total precipitation for New York State is more than 50.2 inches?


(b) What is the probability that next year the total precipitation for New York State is between 41.4 and 47.7 inches?


(c) What is the probability that next year the total precipitation for New York State is between 29.7 and 37.9 inches?


(d) What is the probability that next year the total precipitation for New York State is more than 35.8 inches?


(e) What is the probability that next year the total precipitation for New York State is less than 45.1 inches?


(f) What is the probability that next year the total precipitation for New York State is less than 31.5 inches?

9. According to a website about salaries, the national average salary as of October 2003 for a human resources clerk was $29,932. We assume that the annual salaries for clerks are normally distributed with a standard deviation of $1,890. (Give your answers correct to two decimal places.)

(a) Find the percentage who earn less than $26,780.
%

(b) Find the percentage who earn more than $32,284.

Solution

1.

a)

We get the z score from the given left tailed area. As          
          
Left tailed area =    0.7673      
          
Then, using table or technology,          
          
z =    0.73 [ANSWER]

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b)

Here, the right tailed area is 0.7190, so the left tailed area is 1-0.7190 = 0.2810.

We get the z score from the given left tailed area. As          
          
Left tailed area =    0.281      
          
Then, using table or technology,          
          
z =    -0.58 [ANSWER]  
  
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c)

We get the z score from the given left tailed area. As          
          
Left tailed area =    0.1515      
          
Then, using table or technology,          
          
z =    -1.03 [ANSWER]  

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