Estimating normal weights

A sample of the weights of 100 women indicate that their mean weight is 149 pounds with a standard deviation of 36 pounds.

1. Based on this data, use a normal distribution to estimate the number of women whose weight is between 140 pounds and 150 pounds.
2. Again using this data and assuming that it is normally distributed, approximately what weight is at the 45^{\text{th}} percentile?
3. A histogram of the data is shown below. Based on this, do you see any issues with the use of a normal distribution for the above answers?

1.) 89 women
2.) 144.7 lbs
3.) Yes, the histogram is skewed to the right.

1.) 89 women
2.)145 pounds
3.) Yes, because the histogram is skewed to the right.

1. (area of graph at 140 lbs) - (area of graph at 150lbs)
   .5112 - .4013 = .1099 = 10.99% out of 100 women is about 11 women who weigh between 140 and 150lbs.
   

2. 45% = .45
   qnorm(.45) = -.1256(z score)
   ((Z score x Sd) + mean)
   -.1256(36) + 149 = 144.5lbs
   
   
   

3. You couldn’t use a normal distribution because the data is skewed to the right.

I used just the table (not R) and got the same answers as @Erad.

1. I found the Z score for 140 pounds (-0.25) and 150 pounds (0.028). I looked both of those up on the table to find 40.13% of women weigh 140 or less and 51.2% of women weigh 150 or less. So I subtracted the two to find ~11% of women (11 women total) weigh between 140 and 150 pounds.

2. I found the figure closest to 0.45 in the table and its corresponding z score (-0.12). I plugged this into the formula and found the 45% percentile weight to be ~144.7 pounds.

3. The data is skewed to the right so normal distribution doesn’t apply.

1. 89 women are between 140lbs and 150lbs.
2. 153lbs (My answer differs from the ones I’ve seen so far because in the table I found that .4483 was closer to the .45 than .4522 because .4483 is .0017 away from 45 but .4522 is .022 away from 45. If I am mistaken, please reply and let me know!)
3. Yes, it is skewed to the right.

1. 11.07% or 89 women weigh between 140 and 150 pounds.
2. 144.32 pounds
3. Yes, because the histogram is skewed right.

1. 89 women are between the heights of 140 and 150 pounds
2. 145 pounds at the 45th percentile
3. yes because the histogram is skewed right

1. 89 women
   20 144.4 pounds
   
2. yes, the histogram is skewed to the right

1. 89 women
   2.145 pounds
   
2. Yes, because the histogram is skewed to the right

1. (140-149)/36 = -.25
   pnorm(-.25) = .4013
   (150-149)/36 = .02777778
   pnorm(.0277778) = .5111
   .5111 - .4013 = .1098 = 10.98%
   Approximately 11 women weigh between and 150lbs.
   
   
   
   
   

2. weight = (z * sd) + mean
   45% = .45
   qnorm(.45) = -0.1257
   z = -0.1257
   sd = 36
   (-0.1257(36)) + 149 = 144.47lbs
   
   
   
   
   

3. yes, the histogram is skewed to the right. Therefor, the normal distribution doesn’t apply.

1. 89
2. About 145 pounds
3. Yes, it is skewed to the right.

1. 89 of the surveyed 100 women were between 140 pounds and 150 pounds.
2. Approximately 145 pounds.
3. The normal distribution curve would not fit the graph due to the fact it is skewed to the right.

89 women weigh between 140 and 150 pounds.
144.32 pounds
Yes, because the histogram is skewed right.