1. Determine the total area under the standard normal curve in parts (a) through (c) below.   (a)Find the area under the normal...

1.

Determine the total area under the standard normal curve in parts (a) through (c) below.

(a)Find the area under the normal curve to the left of z= -2 plus the area under the normal curve to the right of z=2

The combined area is _____ (Round to four decimal places)

(b)Find the area under the normal curve to the left of z= -1.54 plus the area under the normal curve to the right of z= 2.54

The combined area is _____(Round to four decimal places)

2.

Find the Z-score such that the area under the standard normal curve to the left is 0.96

            ______ is the Z-score such that the area under the curve to the left is 0.96. (Round to two decimal place)

3.

Find the Z-scores that separate the middle 15% of the distribution from the area in the tails of the standard normal distribution

            The Z- scores are ____

4.

Assume the random variable X is normally distributed with mean= 50 and standard deviation = 7. Compute the probability

            P(X>35)=______ (Round to four decimal places)

5.

Assume that the random variable X is normally distributed, with mean= 53 and standard deviation = 7. Compute the probability

            P(45≥X)= ______ (Round to four decimal places)

6.

Assume the random variable X is normally distributed with mean= 50 and standard deviation= 7. Compute the probability.

            P(35<X<63)=________ (Round to four decimal places)

7.

Assume the random variable X is normally distributed, with mean = 41 and standard deviation = 6. Find the 5^th percentile.

            The 5^th percentile is _______ (Round to two decimal places)

8. The mean incubation time for a type of fertilized egg kept at 100.1 degrees Fahrenheit   is 19 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day.

(a)What is the probability that a randomly selected fertilized egg hatches in less than 17 days?

(b)What is the probability that a randomly selected fertilized egg takes over 21 days to hatch?

(c)  What is the probability that a randomly selected fertilized egg hatches between 18 and 19 days?

(d)Would it be unusual for an egg to hatch in less than 17.5 days? Why?

9.

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and a standar deviation 129 chips.

(a)What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips?

(b)What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips?

(c)  What proportion of bags contains more than 1175 chocolate chips?

(d)What is the percentile rank of a bag that contains 1450 chocolate chips?

10.

The mean incubation time of fertilized eggs is 22 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day.

(a)Determine the 11^th percentile for incubation times

(b)Determine the incubation times that make up the middle 95%

11.

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1261 and a standard deviation of 117.

(a)Determine the 28^th percentile for the number of chocolate chips in a bag

(b)Determine the number of chocolate chips in a bag that make up the middle 97% of bags.

12.

The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 15 minutes and standard deviation of 3 minutes.

(a)The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (Round to two decimal places as needed)

(b)If the automotive center does not want to give the discount to more than 3% of its customers, how long should it make the guaranteed time limit?(Round up to the nearest minute)