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the mean of the sampling distribution

1. Caterer determines that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. If P-hat is the proportion saying that the food is delicious, what is the mean of the sampling distribution p-hat?

2. Farmer counting grasshoppers in his fields, probably not normally distributed due to growing conditions. After several rows the mean number of grasshoppers is 57 SD 12. What is probability that farmer will count 52 or fewer on average on next 40 rows down which he drives his tractor?

3. Rental car agency has 50 cars. Rental rate in winter is 60%. What is probability that in give winter month the rental rate is fewer than 35 cars rented? Use normal distribution to approximate the binomial distribution.

4. Brewery has 12 oz bottle filling machines.  Amount poured by machine is normal distribution mean 12.39 oz  SD 0.04 oz. Company is interested in in reducing the amount of extra beer in its 12 oz bottles. Company seeking to identify the highest 1.5% of the fill amounts poured by machine. For what fill amount are they searching?

5. Certain model of new home distributed with a mean of $150,000. Find percentage of buyers who paid between $150,000-155,000 if standard deviation is $1800.

6. School run known to possess normal distribution with mean 440 sec & SD 60 sec. What is probability that randomly chosen boy can run this race in 302 sec.

7. High temperatures in certain city in the month of August follow uniform distribution over the interval 60-85 F. What is probability that a randomly selected August day has a Temperature exceeding 65 F.

 

 

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