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How do the width and height of a normal distribution change when its mean remains the same but its standard deviation decreases?

For the standard normal distribution, what is the area within \(2.5\) standard deviations of the mean?

Obtain the area under the standard normal curve a. to the right of \(z=1.43\) b. to the left of \(z=-1.65\) c. to the right of \(z=-.65\) d. to the left of \(z=.89\)

Obtain the following probabilities for the standard normal distribution. a. \(P(z>-.98)\) b. \(P(-2.47 \leq z \leq 1.29)\) c. \(P(0 \leq z \leq 4.25)\) d. \(P(-5.36 \leq z \leq 0)\) e. \(P(z>6.07)\) f. \(P(z<-5.27)\)

The Bank of Connecticut issues Visa and MasterCard credit cards. It is estimated that the balances on all Visa credit cards issued by the Bank of Connecticut have a mean of \(\$ 845\) and a standard deviation of \(\$ 270\). Assume that the balances on all these Visa cards follow a normal distribution. a. What is the probability that a randomly selected Visa card issued by this bank has a balance between \(\$ 1000\) and \(\$ 1440 ?\) h. What percentage of the Visa cards issued by this bank have a balance of \(\$ 730\) or more?

quarter), Britons spend an a… # According to a 2004 survey by the telecommunications division of British Gas (Source: http://www. literacytrust.org.uk/Database/texting.html#quarter), Britons spend an average of 225 minutes per day communicating electronically (on a fixed landline phone, on a mobile phone, by emailing, by texting, and so on). Assume that currently such times for all Britons are normally distributed with a mean of 225 minutes per day and a standard deviation of 62 minutes per day. What percentage of Britons communicate electronically for a. less than 60 minutes per day b. more than 360 minutes per day c. between 120 and 180 minutes per day d. between 240 and 300 minutes per day?

According to the records of an electric company serving the Boston area, the mean electricity consumption during winter for all households is 1650 kilowatt-hours per month. Assume that the monthly electric consumptions during winter by all households in this area have a normal distribution with a mean of 1650 kilowatt-hours and a standard deviation of 320 kilowatt-hours. The company sent a notice to Bill Johnson informing him that about \(90 \%\) of the households use less electricity per month than he does. What. is Bill Johnson's monthly electricity consumption?

Find the following binomial probabilities using the normal approximation. a. \(n=140, \quad p=.45, \quad P(x=67)\) b. \(n=100, \quad p=.55, \quad P(52 \leq x \leq 60)\) c. \(n=90, \quad p=.42, \quad P(x \geq 40)\) d. \(n=104, p=.75, \quad P(x \leq 72)\)

In the Energy Information Administration report The Effect of Income on Appliances in U.S. Households (Source: http://www.eia doe.gov/emeu/recs/appliances/appliances. \(\mathrm{html}\) ), it is noted that \(29 \%\) of housing units with an annual income in the \(\$ 15,000\) to \(\$ 29,999\) range own a large-screen television. Assuming that this is true for the current population of housing units with an annual income in the \(\$ 15,000\) to \(\$ 29,999\) range, find the probability that in a random sample of 400 such housing units, the number that have a large screen television is a. exactly 110 b. 124 to 135 c. no more than 105

Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company's management. The company guarantees the refund of money or a replacement for any calculator that malfunctions within two years from the date of purchase. It is known from past data that despite all efforts, \(5 \%\) of the calculators manufactured by this company malfunction within a 2 -year period. The company recently mailed 500 such calculators to its customers. a. Find the probability that exactly 29 of the 500 calculators will be returned for refund or replacement within a 2-year period. b. What is the probability that 27 or more of the 500 calculators will be returned for refund or replacement within a 2 -year period? c. What is the probability that 15 to 22 of the 500 calculators will be returned for refund or replacement within a 2 -year period?