Chapter 4 Quiz - The Normal Distribution

1		Find P(-0.5 < Z < 0.5).
			A)	0.3830
			B)	0.1915
			C)	0.6515
			D)	0.3085
			E)	none of the above
2		Find the probability that a standard normal random variable has a value greater than -1.56.
			A)	0.0332
			B)	0.0594
			C)	0.9406
			D)	0.9668
			E)	none of the above
3		Let X be a normally distributed random variable with mean 100 and standard deviation 20. Find two values, a and b, symmetric about the mean, such that the probability of the random variable being between them is 0.99.
			A)	90.5, 105.9
			B)	80.2, 119.8
			C)	22, 78
			D)	48.5, 151.5
			E)	90.1, 109.9
4		A spark plug manufacturer believes that his plug lasts an average of 30,000 miles, with a standard deviation of 2,500 miles. What is the probability that a given spark plug of this type will last 37,500 miles before replacement?
			A)	0.0228
			B)	0.0114
			C)	0.0013
			D)	0.0714
			E)	0.0833
5		The contents of a particular bottle of shampoo marked as 150 ml are found to be 153 ml at an average, with a standard deviation of 2.5 ml. What proportion of shampoo bottles contain less than the marked quantity? Assume a normal distribution.
			A)	0.2192
			B)	0.1151
			C)	0.4452
			D)	0.0548
			E)	none of the above
6		A grocery store has a mean accounts receivable of $264, with a standard deviation of $55. The accounts receivable are normally distributed. What proportion of all accounts will be greater than $275?
			A)	0.2
			B)	0.1
			C)	0.4207
			D)	0.0793
			E)	0.0228
7		A grocery store has a mean accounts receivable of $264, with a standard deviation of $55. The accounts receivable are approximately normally distributed. Find the value such that 45% of all the accounts exceed this value. That is, find x such that: P(X > x) = 0.45.
			A)	$257.13
			B)	$354.48
			C)	$270.91
			D)	$309.00
			E)	none of the above
8		The IQs of the employees of a company are normally distributed, with a mean of 127 and a standard deviation of 11. What is the probability that the IQ of an employee selected at random will be between 120 and 130?
			A)	0.2389
			B)	0.3453
			C)	0.1064
			D)	0.1325
			E)	0.4638
9		The GMAT scores of students in a college are normally distributed with a mean of 520 and a standard deviation of 41. What proportion of students have a score higher than 600?
			A)	0.9744
			B)	0.2372
			C)	0.4774
			D)	0.0255
			E)	none of the above
10		A normal random variable has a distribution that is:
			A)	always symmetric
			B)	never symmetric
			C)	sometimes symmetric
			D)	symmetric if the mean is positive
			E)	symmetric if the variance is negative
11		What is the probability that a normal random variable with mean 15 and standard deviation 5 will have a value of exactly 25?
			A)	0.0228
			B)	0.0456
			C)	0.9772
			D)	0
			E)	1
12		If X is a normal random variable with mean 15 and standard deviation 10, then the probability that X will have a negative value is:
			A)	0.0668
			B)	0.432
			C)	0.9332
			D)	0.8664
			E)	none of the above