Question

Question 11

A particular fruit's weights are normally distributed, with a mean of 701 grams and a standard deviation of 7 grams.
If you pick one fruit at random, what is the probability that it will weigh between 705 grams and 714 grams.

Question 12

A particular fruit's weights are normally distributed, with a mean of 626 grams and a standard deviation of 20 grams.
The heaviest 15% of fruits weigh more than how many grams?
Give your answer to the nearest gram.

Question 13

A variable xx is normally distributed with mean 20 and standard deviation 8.
Round your answers to the nearest hundredth as needed.

a) Determine the zz-score for x=25x=25.

z=

b) Determine the zz-score for x=15x=15.

z=

c) What value of xx has a zz-score of 0.880.88?

x=

d) What value of xx has a zz-score of −0.3-0.3?

x=

e) What value of xx has a zz-score of 00?

x=

Question 14

The annual rainfall in a certain region is approximately normally distributed with mean 42.7 inches and standard deviation 5.5 inches. Round answers to the nearest tenth of a percent.

a) What percentage of years will have an annual rainfall of less than 44 inches? %
b) What percentage of years will have an annual rainfall of more than 39 inches? %
c) What percentage of years will have an annual rainfall of between 37 inches and 43 inches? %

Question 15

A variable is normally distributed with mean 17 and standard deviation 3. Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed.

a) Find the area to the left of 19.
b) Find the area to the left of 11.
c) Find the area to the right of 16.
d) Find the area to the right of 20.
e) Find the area between 11 and 27.

Question 16

z = 3 is what percentile?

percentile =

State your answer to the nearest tenth of a percent.

Question 17

Noelle and Ashley began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Noelle took a test in Science and earned a 79.4, and Ashley took a test in English and earned a 67.5. Use the fact that all the students' test grades in the Science class had a mean of 75.1 and a standard deviation of 11.5, and all the students' test grades in English had a mean of 66.9 and a standard deviation of 10.6 to answer the following questions.

a) Calculate the z-score for Noelle's test grade.
z=


b) Calculate the z-score for Ashley's test grade.
z=


c) Which person did relatively better?

• Noelle
• Ashley
• They did equally well.

Question 18

A population of values has an unknown distribution with μ=93.3μ=93.3 and σ=65.8σ=65.8. You intend to draw a random sample of size n=39n=39.

What is the mean of the distribution of sample means?
μx=(Please enter an exact answer.)

What is the standard deviation of the distribution of sample means?
σx=(Please report your answer accurate to 2 decimal places.)

Question 19

A population of values has a normal distribution with μ=271.8μ=271.8 and σ=4.6σ=4.6. You intend to draw a random sample of size n=10n=10.
Round zz to two (2) decimal places and final answer to 4 decimal places.

Find the probability that a single randomly selected value is less than 275.
P(x<275)=P(x<275)=

Find the probability that a sample of size n=10n=10 is randomly selected with a mean less than 275.
P(¯x<275)=P(x¯<275)=

Answer 1

11)

µ =    701              
σ =    7              
we need to calculate probability for ,                  
P (   705   < X <   714   )  
=P( (705-701)/7 < (X-µ)/σ < (714-701)/7 )                  
                  
P (    0.571   < Z <    1.857   )   
= P ( Z <    1.857   ) - P ( Z <   0.57   ) =   
0.9684   -    0.7161   =    0.2522   (answer)

12)

µ=   626  
σ =    20  
P(X≤x) =   0.85  
      
z value at 0.85=   1.0364   (excel formula =NORMSINV(0.85))
z=(x-µ)/σ      
so, X=zσ+µ=   1.036   *20+626
X =   647 (answer)

13) a) Z=(X-µ)/σ= (25-20)/8=       0.63

b) Z=(X-µ)/σ= (15-20)/8=       -0.63
c) X=Zσ+µ=0.88*8+20=   27.04
d) X=Zσ+µ=-0.3*8+20=   17.6

e) X=X=Zσ+µ=0*8+20=   20