Men Sample

Men Sample

35% of men wear glasses. what is the probability that, in a random sample of 40 men, 15 or less wear glasses?

This is a past paper stats question, and i can't work out how to work it out. Once I know that, i'll probably be fine. Thanks

The previous answer is very precise and correct, but it requires a lot of calculation. I propose this way of solution.

p=0.35, q=1-p, q=0.65
n=40
15 or less of 40 means that x = 15+0.5

mean = np
mean = 40*0.35=14

SD = √(npq)
SD = √(40*0.35*0.65)=sqrt (5.04)=2.245=2.25

As n > 30, np ≥ 5 and nq ≥ 5, we can use the normal approximation to the binomial applying continuity correction of 0.5 for using a continuous distribution for a discrete one.

The critical ratio for the lower tail:
z = [(15+0.5) - 14)]/ 2.25 = 0.667

It cuts off the lower 74.76 % percent of the normal curve. The probability is 0.75.

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Breast cancer is one of the most common cancers in women with 41,000 cases being diagnosed each year as well as about 300 men. The chances of developing breast cancer are higher in older women but lower in those who have children at an early age and have breast fed their children. It's also important to develop some breast cancer tests of your own, that you can do on a regular basis in between mammograms. As soon as you hit puberty, it's a good idea to conduct self breast cancer tests as this begins the period where your chances of getting breast cancer begin.

There are several symptoms:

* a lump-it will usually be small, firm and painless

* veins that become more prominent on one or both breasts just under the skin surface

* a depression in any area of the breast surface that was not there before.

LIQUID DISCHARGE FROM THE NIPPLE:- Another possible symptom of breast cancer is nipple discharge. This discharge can be in the form of either blood or pus that is clear, green or yellow. However, like the above symptoms discharge from the nipple is generally down to other causes.

A CHANGE IN THE BREAST SKIN'S APPEARANCE:- If your breast skin starts to look different this could be a sign of breast cancer. This type of cancer may cause your breast skin to become dimpled (like an orange peel), wrinkled, swollen or inflamed. However, like with lumps a change in the breast skin's appearance can be down to other factors.

Following tests may be done:

Mammography - a low dose x-ray of the breast tissue

Ultrasound - the use of sound waves to build up a picture of the breast tissue

Colour Doppler ultrasound - shows the blood supply to the area to determine the difference between a cancer and a benign lump

Needle (core) biopsy - a needle is used to take a small piece of tissue from the affected area

Fine needle aspiration - a needle and syringe are used to take a cell sample form the affected area

Blood tests - general health check to see how the liver and kidneys are working and check for the presence of cancer producing chemicals in the blood

Excision biopsy - surgery where the whole lump is removed and sent for examination

One-stop clinics - Clinics where all relevant tests are done together and results are processed while you wait.

Diet:

During our body's process of converting food to energy, we create free radicals in our body. These free radicals are damaging to our cells and DNA if we don't combat them. Left unchecked, free radicals contribute to speeding up the aging process and to causing diseases such as cancer, heart attack and stroke.

Anti-oxidants, however, can help us combat these free radicals, and a diet in anti-oxidants is linked with preventing cancer, heart disease and stroke. So, doctors recommend a diet high in anti-oxidants – which means eating lots of fresh fruits and vegetables and drinking green tea each day.

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