Question

THE BOLDED LETTER AND NUMBER IS THE GIVEN ANSWER. ONE OF THE BOLDED ANSWERS ARE INCORRECT, WHICH ONE IS INCORRECT AND WHAT IS THE CORRECT ANSWER?

Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years. You want to set the warranty on your product so that you do not have to replace more than 5% of the hot water heaters that you sell. How many years should you claim on your warranty?

	a.	13.09
	b.	10.53
	c.	12.91
	d.	15.47
	e.	22.88

In a highway construction zone with a posted speed limit of 40 miles per hour, the speeds of all vehicles are normally distributed with a mean of 46 mph and a standard deviation of 3 mph. Find the probability that the speed of a random car traveling through this construction zone is more than 45 mph.

	a.	0.6306
	b.	0.1258
	c.	0.4172
	d.	0.3694
	e.	0.5828

The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 6.7 minutes and a standard deviation of 2.1 minutes. Find the probability that the delivery time for a random order at this restaurant is between 7 and 8 minutes.

	a.	0.7851
	b.	0.8247
	c.	0.2150
	d.	0.1880
	e.	0.1753

The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (Source: American Dietetic Association). This distribution is approximately bell-shaped and symmetric. If an individual is randomly selected, find the probability that the number of pounds of red meat they consume each year will be less than 200 pounds.

	a.	0.0721
	b.	0.4279
	c.	0.0014
	d.	0.9986
	e.	0.5721

The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6.0 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.75 ounces and a standard deviation of 0.11 ounces. What percentage of pucks produced at this factory cannot be used by the National Hockey League?

	a.	0.3321
	b.	0.6679
	c.	0.0230
	d.	0.9770
	e.	0.2741

1. The distribution of scores on a statistics final exam is approximately normal with a mean of 62 and a standard deviation 11. Find the z-score for a score of 77 on the statistics final exam.

	a.	71.36
	b.	0.66
	c.	-0.66
	d.	1.36
	e.	-1.36

Answer 1

Solution:-

Given that,

1) mean = = 13

standard deviation = =1.5

5% = 0.05

P(Z > z ) = 0.05

1- P(z < z) =0.05

P(z < z) = 1-0.05 = 0.95

z = 1.645

Using z-score formula,

x = z * +

x =1.645*1.5+13

x = 15.47 years

d) Answer = 15.47

2)

mean = = 46

standard deviation = = 3

P(x >45) = 1 - p( x< 45)

=1- p [(x - ) / < (45 - 46) / 3]

=1- P(z < -0.33)

= 1 - 0.3707 = 0.6306

probability = 0.6306

Answer =a ) 0.6306

3)

mean = = 6.7

standard deviation = = 2.1

P( 7< x < 8) = P[(7 - 6.7)/2.1 ) < (x - ) /  < (8 -6.7) /2.1 ) ]

= P( 0.14< z < 0.62)

= P(z <0.62 ) - P(z <0.14 )

Using standard normal table

= 0.7324 - 0.5557 = 0.1753

Probability = 0.1753

Answer = e) 0.1753

4)

mean = = 196

standard deviation = =22

P(x <200 ) = P[(x - ) / < (200 -196) /22 ]

= P(z < 0.182)

= 0.5721

probability =0.5721

Answer = e) 0.5721

5)

mean = = 5.75

standard deviation = = 0.11

P( 5.5< x < 6.0 ) = P[(5.5 - 5.75)/ 0.11) < (x - ) /  < (6.0 -5.75) /0.11 ) ]

= P( -2.27< z < 2.27 )

= P(z < 2.27 ) - P(z < 2.27 )

Using standard normal table

= 0.9884 - 0.0116 = 0.9770

Probability = 0.9770

Answer = d) 0.9770

6)

mean = = 62

standard deviation = = 11

x = 77

z score = x - u /

= 77 -62 / 11

= 1.36

Answer = d) 1.36