Question

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.9 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median recovery time? days

c. What is the Z-score for a patient that took 4.4 days to recover?

d. What is the probability of spending more than 2.5 days in recovery?

e. What is the probability of spending between 2.9 and 3.7 days in recovery?

f. The 90th percentile for recovery times is days.

Private nonprofit four-year colleges charge, on average, $27,166 per year in tuition and fees. The standard deviation is $7,402. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 25,605 per year.

c. Find the 60th percentile for this distribution. $ (Round to the nearest dollar.)

The average number of words in a romance novel is 64,416 and the standard deviation is 17,228. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the proportion of all novels that are between 59,248 and 71,308 words.

c. The 80th percentile for novels is words. (Round to the nearest word)

d. The middle 50% of romance novels have from words to words. (Round to the nearest word)

According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.4 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that the person is between 59.3 and 61.7 inches.

c. The middle 40% of Martian heights lie between what two numbers?
Low: inches
High: inches

Answer 1

Ansa: the distribution of X is

X ~ N(=3,^2=1.9^2)

Ansb>

For normal distribution ,

Mean = median.

So,

the median recovery time==3 days

Ansc:

z = ( X - Mean) / Standard deviation

= ( 4.4 - 3 ) / 1.9

= 0.7368

Ansd:

P(X>2.5)=P((x-)/>(2.5-3)/1.9))

=P(Z>-0.26)

=0.6038

#P(X>2.5)=0.6038

Anse:

P(2.9<x<3.7)=P((2.9<3)/1.9<(x-)/<(3.7-3)/1.9))

=P(-0.05<Z<0.37)

=P(Z<0.37)-P(Z<-0.05)

=0.6437-0.4790

=0.1647

#P(2.9<x<3.7)=0.1647