5. The mean lifetime of laptop computers produced by one company is 4.6 years with a standard deviation of 1.1 years. Consider random samples of 55 laptop computers. What is the probability that the mean lifetime of the sample is at most 4 years? Describe the sampling distribution of the sample mean to verify that the distribution is normal. 6. A national caterer determined that 87% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained. Describe the sampling distribution of the sample proportions. Can we assume the sampling distribution of the sample proportion is normal? How do you know? What is the mean of the sampling distribution of sample proportions? . What is the standard deviation of the sampling distribution of sample proportions? What is the probability that less than 85% of the sample of 144 people said the caterer's food was delicious? Is this unusual? 7. A local florist says that 85% of all flowers sold for Valentine's Day are roses. Consider a random sample of 150 orders for Valentine's Day flowers. What is the probability that less than 80% of the orders in the sample are for roses? Describe the sampling distribution of the sample proportions to confirm the distribution is normal. 8. A popular restaurant downtown say that 20% of diners order the daily special. Consider a random sample of 128 people who dined at the restaurant. What is the probability that the proportion of diners who ordered the special is less than 19%? Describe the sampling distribution of the sample proportions to confirm the distribution is normal