1)A particular fruit's weighs are normally distributed, with a mean of 341 grams and a standard deviation of 23 grams.If you pick 19 fruit at random, what is the probability that their mean weight will be between 342 grams and 350 grams.

2)A particular fruit's weighs are normally distributed with a mean of 583 grams and a standard deviation of 16 grams. If you pick 29 fruits at random, then 16% of the time, their mean weight will be greater than how many grams? Give the answer to the nearest gram.

3)Suppose that the efficacy of a certain drug is 0.62 , consider the sampling distribution(sample size n=201) for the proportion of patients cured by this drug.

a)what is the mean of this distribution?

b)what is the standard error of this distribution? Round answer to four decimal places.

4)According to a 2009 Reader's Digest article, people throw away approximately 10% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 174 grocery shoppers to investigate their behavior. What is the probability that the sample proportion exceeds 0.19 . Give answer as a number accurate to four decimal places.

5)Scores for a common standardized college aptitude test are normally distributed with a mean of 486 and a standard deviation of 99. Randomly selected men are given a Test preparation course before taking this test. Assume, for sake of argument, that the preparation course has no effect.

a)If 1 of the men is randomly selected, find the probability that his score is at least 526.8

P(X > 526.8 )=

b)If 17 of the men are randomly selected, find the probability that their mean score is at least 526.8

P(M > 526.8)=

6)A population of values has a normal distribution with mean=66 and standard deviation= 4.2 , you intend to draw a random sample of size n=198

a)find the probability that a single randomly selected value is greater than 65.7

P(X > 65.7 )=

b)find the probability that a sample of size n=198 is randomly selected with a mean greater than 65.7

P(M > 65.7 )=

Enter the answers as numbers accurate to four decimal places, answers obtained using exact z-scores or z-scores rounded to three decimal places are acceptable.

7)The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality.His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.1 years and a standard deviation of 0.4 years. He then randomly selects records on 27 laptops sold in the past and finds that the mean replacement time is 3.9 years.

a) Assuming that the laptop replacement times have a mean of 4.1 years and a standard deviation of 0.4 years, find the probability that 27 randomly selected laptops will have a mean replacement time of 3.9 years or less. Enter the answer as a number accurate to four decimal places.

8)A food Marketing institute found that 56% of households spend more than $125 a week on groceries. Assume the population proportion is 0.56 and a simple random sample of 119 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is more than 0.51? Round any z-values you calculate to four decimal places to match wamap's approach and calculations.

9)Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans.

a)what assumptions must be true to be able to approximate the sampling distribution with a normal model? Assumptions:

b)what are the mean and standard deviation of this model? Accurate answers to three decimal places.

c)what is the probability that over 10% of these clients will not make timely payments?