1) The time required to assemble an electronic component is normally distributed

Question

1) The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 22 minutes and 15 minutes, respectively. Use Table 1.

Find the probability that a randomly picked assembly takes between 17 and 24 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

It is unusual for the assembly time to be above 44 minutes or below 4 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

  Proportion of assembly times

2) The manager of a night club in Boston stated that 90% of the customers are between the ages of 22 and 26 years. If the age of customers is normally distributed with a mean of 24 years, calculate its standard deviation. (Round your answer to 2 decimal places.)

Standard deviation

3) A construction company in Naples, Florida, is struggling to sell condominiums. In order to attract buyers, the company has made numerous price reductions and better financing offers. Although condominiums were once listed for $400,000, the company believes that it will be able to get an average sale price of $299,000. Let the price of these condominiums in the next quarter be normally distributed with a standard deviation of $14,000. Use Table 1.

What is the probability that the condominium will sell at a price (i) Below $285,000?, (ii) Above $320,000? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

The company is also trying to sell an artist’s condo. Potential buyers will find the unusual features of this condo either pleasing or objectionable. The manager expects the average sale price of this condo to be the same as others at $299,000, but with a higher standard deviation of $21,000. What is the probability that this condo will sell at a price (i) Below $285,000?, (ii) Above $320,000? (Round your answers to 4 decimal places.)

1) The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 22 minutes and 15 minutes, respectively. Use Table 1.

Explanation / Answer

a)P(17<X<24)=P((17-22)/15<X<(24-22)/15)=P(-0.3333<Z<0.1333)=0.5530-0.3694=0.1836

b)P(X<4)+P(X>44)= P(Z<(4-22)/15)+P(Z>(44-22)/15)=P(Z<-1.2)+P(Z>1.4667)=0.1151+0.0712=0.1863

no it is not unusual as it is greater then 0.05.

2)z score =1.64485

std deviation=(X-mean)/zscore =(26-24)/1.64485=1.2159

3)a)P(X<285000)=P(Z<(285000-299000)/14000)=P(Z<-1)=0.1587

P(X>320000)=P(Z>1.5)=0.0668

b)P(X<285000)=P(Z<-0.6667)=02525

P(X>320000)=P(Z>1)=0.1587

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