Deck 34: Normal Distribution

Question 1

If the normal distribution is to be used as an approximation to the binomial with n = 200 and p = 0.78 what value should be used to approximate the standard deviation (1 decimal place)?

A) 5.8
B) 5.9
C) 6.0
D) 6.1

Answer 1

5.9

Question 2

If the probability that a Z-score lies between 0 and 2 is 0.452 then what is the probability that Z < 2?

A) 0.4772
B) 0.5
C) 0.9772
D) 0.0228

Answer 2

0.9772

Question 3

Analysis of a sample of 50 of the second quarter sales of a Dubai fashion store shows a difference ( - ) of AED 236, z = +2.37 indicating that the difference is significant. Calculate the standard deviation of the sample (1 decimal place).

A) AED 697.3
B) AED 704.1
C) AED 723.6
D) AED 734.9

Answer 3

AED 704.1

Question 4

Assuming a confidence interval of 95% (z = 1.96), calculate the width of the confidence interval for n = 65, = 24.5, s = 4.5 (1 decimal place)

A) 24.5 ± 0.8
B) 24.5 ± 0.9
C) 24.5 ± 1.0
D) 24.5 ± 1.1

Question 5

Calculate the Z-score for a value of 34 when mean = 24 and standard deviation = 4

A) 2.0
B) 2.2
C) 2.5
D) 2.8

Question 6

Which of the following statements about the normal distribution are NOT true?

A) The normal distribution is symmetrically shaped
B) The normal distribution is centred around the mean
C) The normal distribution shows a clustering of values around the mean
D) The normal distribution is not suitable for use with continuous data

Question 7

What name is given to a value that has been standardized?

A) Mean
B) Z-score
C) Standard Deviation
D) Variance

Question 8

Last year average wages in an Indian firm were INR 109,658, a sample of 30 employees in the same firm this year gives an average wage of INR 110,986 (standard deviation INR 1,234). Is this evidence of a significant difference in wages?

A) No, -1.96 < z < 1.96
B) Yes, they have gone down, z < -1.96
C) Yes, they have gone up z > 1.96
D) There is no evidence of a significant difference

Question 9

A sample of components made by a factory in China shows that 6 out of a sample of 50 were found to be faulty. What is the width of a 95% confidence interval (z = 1.96) for the defect rate (2 decimal places)?

A) 0.12 ± 0.06
B) 0.12 ± 0.09
C) 0.12 ± 0.12
D) 0.12 ± 0.15

Question 10

The diameter of holes drilled into flat-pack furniture is normally distributed with a mean of 5mm and a standard deviation of 0.15mm. If a single item of furniture has 50 holes in it, how many have a diameter of more than 5.2mm (to the nearest whole number)?

A) 5
B) 6
C) 7
D) 8