Probability question

[statisticsisawesome]

Can someone please verify if my answers are correct for the below questions?

People have one of four different blood types – O, A, B or AB. Suppose 49% of the population have blood type O, 38% have type A, 10% have type B and 3% have type AB.
a) What is the probability that a randomly selected person
i) does not have type O blood? 0.51
ii) has type A or type B blood? 0.48
iii) is neither type O nor type A? 0.13
b) Among 4 random patients, what is the probability that
i) all have type O? (0.49)^4 = 0.05764801
ii) none of them are type A? (0.62)^4 = 0.14776336
iii) at least one person is type B? 1 - ((0.90)^4) = 0.3439
iv) the third patient only is type A? 0.62*0.62*0.38*0.62 = 0.09056464

Suppose a new cancer treatment has a 20% chance of curing a patient
a) For 5 cancer patients, what is the probability that:
i) none will be cured? 5C0 * (0.2)^0 * (0.8)^5 = 0.32768
ii) exactly 2 patients will be cured? 5C2 * (0.2)^2 * (0.8)^3
iii) at least 2 patients will be cured? P(X = 1) = 5C1 * (0.2)^1 * (0.8)^4 = 0.4096
P(X = 0) = 0.32768
P(X >=2) = 1 - (0.32768 + 0.4096) = 0.26272

b) For 500 patients
i) how many would you expect to be cured by the treatment? 500 * 0.20 = 100 patients
ii) what is the probability that more than 75 of the patients are cured?
variance = np(1-p) = (500*0.20)(0.8) = 80
so the standard deviation = sqrt(80)
using normal distribution with mean as 100 and standard deviation as sqrt(80)
P(X > 75) = 0.9974

Thanks!

 

[Dr.Peterson]

I didn't check all your numerical answers, but the work all looks right. (Thanks for showing work!)

 

[statisticsisawesome]

I didn't check all your numerical answers, but the work all looks right. (Thanks for showing work!)

Would you please be able to check the numerical answers as well?
Thanks

 

[statisticsisawesome]

2.8 A survey on the drinking habits of adults asked the participants how many days a week they consumed alcohol, as well as the type and quantity of alcohol consumed. Of the 755 adults surveyed, 491 said they consumed alcohol at least twice a week
a) Create a 95% confidence interval for the true proportion of adults who consume alcohol at least twice a week, and interpret the interval
P hat = 491/755
therefore Q hat = 264/755
(491/755) - 1.96*sqrt(((491/755)*(264/755)))/(755))) < P < (491/755) + 1.96*sqrt(((491/755)*(264/755)))/(755)))
= 0.616315509 < P < 0.684346743
therefore we are 95% confident that between 61.63% and 68.44% drink alcohol atleast twice a week

b) Based on your confidence interval, comment on the accuracy of a media report stating that 70% of adults consume alcohol at least twice a week.
Not very accurate since 70% is not within the confidence interval (61.63%, 68.44%)
Can someone please verify if my answers for the above question are correct?
Thanks

 

[statisticsisawesome]

Can I please have some help with this question below?
2.2 What’s the design? Read the brief description related to a statistical study below, and
a) explain why it is an experiment rather than an observational study.

Runners recovering from lower leg fractures were randomly allocated to three different training programs. Half of each group also followed a high calcium diet. Bone density measurements were taken for all subjects
b) identify the factor(s) in the experiment and the number of levels for each.
c) give the total number of treatments.
d) state the response variable(s) measured.
e) explain whether it was blind, or double-blind