# Probability, Normal Distribution, Binomial Probabilities, Confidence Intervals, and Critical Values

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1. A brand name has 80% recognition rate. If the owner of the brand wants to verify that rate beginning with a small sample of 15 randomly selected consumers, find the probability that exactly 12 of the 15 consumers recognize the brand name. Also find the probability that the number who recognize the brand name is not 12.

The probability that exactly 12 of the 15 consumers recognize the brand name is ____

The probability that the number who recognize the brand name is not 12 is_____

2. Women's heights are normally distributed with mean 63.2in and standard deviation of 2.5in. A social organization for tall people has a requirement that women must be at least 69in tall. What percentage of women meet that requirement?

The percentage of women that are taller than 69in is ____% (Use the standard normal table negative and positive z-scores)

3. A) with n=11 and p=0.6, find the binomial probability P(6) by using a binomial probability table. (B) If np ≥ 5 and nq ≥ 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial; if np < 5 or nq < 5, then state the normal approximation cannot be used.

a) Find the probability by using a binomial probability table

P(6)=____

b) What's P(6)=_____ or The normal distribution cannot be used

4. Using the simple random sample of weights of women from data set, we obtain these sample statistics: n=45 and x =149.47 lb. Research from other sources suggests that the population of weights of women has a standard deviation given by ơ =30.82lb.

a. Find the best point estimate of the mean of all women.

b. Find a 99% confidence interval estimate of the mean weight of all women.

a The best point estimate is ___lb.

b.The 99% confidence interval estimate is __lb < µ <__lb

5. The heights were measured for nine supermodels. They have a mean of 69.8in. and a standard deviation of 1.9in. Use the traditional method and a 0.01 significance level to test the claim that supermodels have heights with a mean that is greater than the mean of 63.6in. for women from the general population.

Therefore do you Reject or Do not reject and is it greater or not greater than the critical value 2.896?

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The expert examines probability, normal distributions, and binomial probabilities for randomly selected consumers. The percentage of women who are taller than 69in are given.

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1. A brand name has 80% recognition rate. If the owner of the brand wants to verify that rate beginning with a small sample of 15 randomly selected consumers, find the probability that exactly 12 of the 15 consumers recognize the brand name. Also find the probability that the number who recognize the brand name is not 12.

The probability that exactly 12 of the 15 consumers recognize the brand name is

Use binomial distribution

p=0.80

q=1-p=1-0.8=0.20

P(x=12)=12C15p^12*q^3 = (15*14*13)/(1*2*3)*(0.8)^12*(0.2)^3=0.2501

The probability that the number who recognize the brand name is not 12 is_____

P(x≠12)=1-P(x=12)=1-0.2501=0.7499

2. Women's heights are normally distributed with mean 63.2in and standard deviation of 2.5in. A social organization for ...

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