Question

I. Assume that z is normally distributed with a specified mean and standard deviation. Find the indicated probabilities: c, p(x 120); μ 100 ; ơ--15 2. Find z such that 28% of the standard normal curve lies to the right of z. 3. A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter of blood. After a 12- hour fast, the random variable x will have a distribution that is approximately normal with a mean μ 8 standard deviation ơ-# 25, After 50 years, these tend to increase. 5 and a Find the probability that, an adult under 50 years of age selected at random after a 12 hour fast will have a) Will have a glucose level greater than 60 b) Will have a glucose level between 65 and 110 4. Per Capita Spending on Health Care The average per capita spending on health care in the United States is $5274. If the standard deviation is $600 and the distribution of health care spendng is approximately normal, what is the probability that a randomly selected person spends more than $6000? 5. High Cholesterol Levels The serum cholesterol levels in men aged 18 24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7. Units are in mg/ 100 ml, and the data are based on the National Health Survey а) If 15 men aged 18-24 is randomly selected, find the probability that their me serum cholesterol level is greater than 160, a value considered to be "moderate high.

Answer 1

1) P(X < A) = P(Z < (A - mean)/stadnard deviation)

a) P(2 $\small \leq$ x $\small \leq$ 6) = P(x < 6) - P(x < 2)

= P(Z < (6 - 4)/2) - P(Z < (2 - 4)/2)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

b) P(8 $\small \leq$ x $\small \leq$ 12) = P(x < 12) - P(x < 8)

= P(Z < (12 - 15)/3) - P(Z < (8 - 15)/3)

= P(Z < -1) - P(Z < -2.33)

= 0.1587 - 0.0099

= 0.1488

c) P(x $\small \geq$ 120) = 1 - P(X $\small \leq$ 120)

= 1 - P(Z < (120 - 100)/15)

= 1 - P(Z < 1.33)

= 1 - 0.9082

= 0.0918

2) Area to the right of z = 0.28

Area to the left of z = 1 - 0.28 = 0.72

From the standard normal distribution table, take value of Z corresponding to 0.72

Z = -0.58