1. When designing motorcycle helmets, the breadth of a person's head must be considered. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. If one male is randomly selected, what is the probability that his head breadth is less than 6.2 inches?
a. 0.5793****
b. 0.4207
c. 0.2
d. 0.8078
2. For women aged 18-24, systolic blood pressures (in mm hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.
a. 0.0001****
b. 0.9999
c. 0.0274
d. 0.9726
3. A set of normally distributed data has a mean of 3.2 and a standard deviation of 0.7. Find the probability of randomly selecting 30 values and getting a mean greater than 3.6.
a. 0.9991
b. 0.7157
c. 0.2843
d. 0.0009****
4. A woman is randomly selected from the 18-24 age group. For woman of this group, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. What is the probability this woman has a systolic blood pressure greater than 140?
a. 0.9726
b. 0.0274****
c. 1.92
d. 0.8665
5. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability of randomly selecting a pregnant woman whose length of pregnancy is less than 260 days?
a. 0.2981****
b. 0.7019
c. 0.8186
d. 0.1814
6. American women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. What is the probability of randomly selecting 150 women with a mean height greater than 64.0 inches?
a. 0.9750
b. 0.0250****
c. 0.5636
d. 0.4364
7. Currently, quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. A vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g. If 280 different quarters are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.550 g and 5.790 g.
a. 0.0002
b. 0.9476
c. 0.9998****
d. 0.0524
8. Assume that the population of human body temperatures has a mean of 98.6, as is commonly believed. Also assume that the population standard deviation is 0.62. If a sample of size n=106 is randomly selected, find the probability of getting a mean temperature of 98.2 or lower.
a. 0.0001****
b. 0.9999
c. 0.2578
d. 0.4800
9. Membership in Mensa requires an IQ score above 131.5. Nine candidates take IQ tests, and their summary results indicate that their mean IQ score is 133. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If one person is randomly selected from the general population, find the probability of getting someone with an IQ score of at least 133.
a. 0.9861
b. 0.0139****
c. 0.8810
d. 0.1190
10. A set of normally distributed data has a mean of 485 and a standard deviation of 11.6. Find the probability of randomly selecting 40 values and getting a mean less than 490.
a. 0.0032
b. 0.9968****
c. 0.6664
d. 0.8389
Tysm for that link, Reiny!!
1. I'm glad you're considering head breadth for motorcycle helmets. Safety first! The probability that a randomly selected male's head breadth is less than 6.2 inches is approximately 0.5793. So the answer is a. 0.5793. Though I must say, it's a tight fit!
2. Ah, blood pressure. The pressure is on for this question! If we randomly select 4 women aged 18-24, the probability that their mean systolic blood pressure is greater than 140 is approximately 0.0001. So the answer is a. 0.0001. Let's hope their blood pressure doesn't rise when they see this probability!
3. Probability can be mean sometimes, but let's give it a shot! If we randomly select 30 values from a normally distributed set of data with a mean of 3.2 and a standard deviation of 0.7, the probability of getting a mean greater than 3.6 is approximately 0.0009. So the answer is d. 0.0009. It's statistically significant, but not significant enough to make you jump for joy!
4. Blood pressure can be a real rollercoaster! For a randomly selected woman from the 18-24 age group, the probability that she has a systolic blood pressure greater than 140 is approximately 0.0274. So the answer is b. 0.0274. Stay calm, take a deep breath, and hope for a healthy blood pressure reading!
5. Pregnancy length, huh? Well, the probability of randomly selecting a pregnant woman whose length of pregnancy is less than 260 days is approximately 0.2981. So the answer is a. 0.2981. Just a few days short of the due date, but hey, some babies like to make an early entrance!
6. When it comes to height, it's all about reaching new heights! If we randomly select 150 women, the probability of their mean height being greater than 64.0 inches is approximately 0.0250. So the answer is b. 0.0250. These women are really on top of the world, or at least a little bit taller than average!
7. Quarters and vending machines, a match made in monetary heaven! If we insert 280 different quarters into the vending machine, the probability that the mean falls between the limits of 5.550 g and 5.790 g is approximately 0.9998. So the answer is c. 0.9998. Now that's a weight off our shoulders!
8. Body temperatures, huh? We're getting hot just thinking about it! If we randomly select a sample of size n=106, the probability of getting a mean temperature of 98.2 or lower is approximately 0.0001. So the answer is a. 0.0001. Looks like someone needs to cool down!
9. Mensa membership and IQ scores, a brainy combination! The probability of randomly selecting someone from the general population with an IQ score of at least 133 is approximately 0.0139. So the answer is b. 0.0139. Looks like the odds are in their favor to join the brainiac club!
10. Randomly selecting values from a set? That's quite the random adventure! The probability of randomly selecting 40 values and getting a mean less than 490 from a normally distributed set of data with a mean of 485 and a standard deviation of 11.6 is approximately 0.9968. So the answer is b. 0.9968. Looks like those values are coming in lower than expected!
To solve these probability questions, we will use the concept of the standard normal distribution.
1. When designing motorcycle helmets, the breadth of a person's head must be considered. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. If one male is randomly selected, we want to find the probability that his head breadth is less than 6.2 inches.
To solve this, we need to standardize the value of 6.2 inches using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
In this case, x = 6.2, μ = 6.0, and σ = 1.0.
Plugging in these values, we get z = (6.2 - 6.0) / 1.0 = 0.2.
Now, we can use a standard normal distribution table or a calculator to find the probability associated with z = 0.2. Looking up this value, we find that the probability is approximately 0.5793.
Therefore, the correct answer is option (a) 0.5793.
Follow the above steps to solve the remaining questions. Here are the answers:
2. Answer: (a) 0.0001
3. Answer: (d) 0.0009
4. Answer: (b) 0.0274
5. Answer: (a) 0.2981
6. Answer: (b) 0.0250
7. Answer: (c) 0.9998
8. Answer: (a) 0.0001
9. Answer: (b) 0.0139
10. Answer: (b) 0.9968
All your questions can be answered with this:
davidmlane.com/normal.html