Quiz 5

1.  Find the​ Z-score such that the area under the standard normal curve to the left is 0.52.

____  is the​ Z-score such that the area under the curve to the left is .

2.  Find the value of

. 

$Z_{0.25 }=$

3.  Suppose the birth weights of​ full-term babies are normally distributed with mean 3450 grams and standard deviation

. Complete parts​ (a) through​ (c) below.
​(a) Draw a normal curve with the parameters labeled. Choose the correct graph below.

​(b) Shade the region that represents the proportion of​ full-term babies who weigh more than 4450 grams. Choose the correct graph below.

​(c) Suppose the area under the normal curve to the  of X = 4450 is 0.0228. Provide an interpretation of this result. Select the correct choice below and fill in the answer box to complete your choice.  ​(Type a whole​ number.)

1. The probability is 0.0228 that the birth weight of a randomly chosen​ full-term baby in this population is less than ___ grams.
2. The probability is 0.0228 that the birth weight of a randomly chosen​ full-term baby in this population is more than ____ grams.

4.  Assume that the random variable X is normally​ distributed, with mean

and standard deviation 

. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

$P\left(X\le 46\right)$

Which of the following shaded regions corresponds to 

$P\left(4\le 46\right)$

=

5.  The graph of a normal curve is given. Use the graph to identify the value of  and .

The value of

is

The value of

is

6. The lengths of a particular​ animal’s pregnancies are approximately normally​ distributed, with mean 

260  days and standard deviation  

days.
​(a) What proportion of pregnancies lasts more than 280  ​days?
​(b) What proportion of pregnancies lasts between 252 and  272 ​days?
​(c) What is the probability that a randomly selected pregnancy lasts no more than  256 ​days?
​(d) A​ “very preterm” baby is one whose gestation period is less than 220  days. Are very preterm babies​ unusual?

​(a) The proportion of pregnancies that last more than 280 days is _____ Round to four decimal places as​ needed.)

​(b) The proportion of pregnancies that last between 252  and  272 days is  _____ ​(Round to four decimal places as​ needed.)

​(c) The probability that a randomly selected pregnancy lasts no more than  days is ____ ​(Round to four decimal places as​ needed.)

​(d) A​ “very preterm” baby is one whose gestation period is less than 220 days. Are very preterm babies​ unusual?

The probability of this event is ____ 0.0062​, so it ____  be unusual because the probability is ___  than 0.05.  ​(Round to four decimal places as​ needed.)

7.  Fill in the blank to complete the statement.
The notation

is the​ z-score that the area under the standard normal curve to the right of

is​ _______.

8.  One graph in the figure represents a normal distribution with mean

 and standard deviation

. The other graph represents a normal distribution with mean

and standard deviation 

. Determine which graph is which and explain how you know.
Choose the correct answer below.

1. Graph A has a mean of
   $\mu = 11$

    and graph B has a mean of

   $\mu = 16$

    because a larger mean shifts the graph to the left. 

2. Graph A has a mean of
   $\mu = 11$

    and graph B has a mean of

   $\mu = 16$

    because a larger mean shifts the graph to the right. 

3. Graph A has a mean of  
   $\mu = 16$

   and graph B has a mean of  

   $\mu = 11$

   because a larger mean shifts the graph to the right.

4. Graph A has a mean of  
   $\mu = 16$

   and graph B has a mean of

   $\mu = 11$

    because a larger mean shifts the graph to the left.

9. Assume the random variable X is normally distributed with mean

 and standard deviation

. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Which of the following normal curves corresponds to 

$P\left(X>43\right) =$

10.  Find the​ Z-score such that the area under the standard normal curve to the right is 0.22.

The approximate​ Z-score that corresponds to a right tail area of  is ____

11.  Determine whether the following graph can represent a normal density function.

Could the graph represent a normal density​ function?

1. No
2. Yes

12.  Assume the random variable X is normally distributed with mean

 and standard deviation

. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

$P\left(34<X<63\right)$

Which of the following normal curves corresponds to 

$P\left(34<X<63\right)$

13.  The mean incubation time of fertilized eggs is  21 days. Suppose the incubation times are approximately normally distributed with a standard deviation of  1 day.
​(a) Determine the 15th percentile for incubation times.
​(b) Determine the incubation times that make up the middle 39 ​%.

​(a) The th percentile for incubation times is ___ days. ​(Round to the nearest whole number as​ needed.) 
​(b) The incubation times that make up the middle ​% are ___ to ___ days.  ​(Round to the nearest whole number as needed. Use ascending​ order.) 

14.  The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon.​ (a) What proportion of hybrids gets over 62 miles per​ gallon? (b) What proportion of hybrids gets 52 miles per gallon or​ less?  proportion of hybrids gets between  58 and 61 miles per​ gallon? (d) What is the probability that a randomly selected hybrid gets less than 46  miles per​ gallon?

​(a) The proportion of hybrids that gets over 62 miles per gallon is ____ ​(Round to four decimal places as​ needed.)
​(b) The proportion of hybrids that gets  miles per gallon or less is ____ ​(Round to four decimal places as​ needed.)
​(c) The proportion of hybrids that gets between  and  miles per gallon is ____ ​(Round to four decimal places as​ needed.)
​(d) The probability that a randomly selected hybrid gets less than  miles per gallon is ____ ​(Round to four decimal places as​ needed.)

15.  Fill in the blank to complete the statement.
The area under the normal curve to the right of

 equals​ _______.