Question

Pete Tagaris Enterprises is one of the largest privately held agricultural operations in the United States, with a sizable irrigated hay land in the state of Washington. A recent study of the weight of hay bales at their Washington operation shows that bale weight is normally distributed with a mean of 80.5 pounds and a standard deviation of 7.2 pounds. A hay bale is considered too heavy if it weighs more than 90 pounds. What is the probability that a single hay bale selected at random will weigh more than 90 pounds? ANSWER: (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules) A hay bale is considered too light if it weighs less than 72 pounds. What is the probability that a single hay bale selected at random will weigh less than 72 pounds? ANSWER: (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer as a percentage to 4 decimal places, using conventional rounding rules) If the Tagaris managers had their way, the hay bales would ideally weigh between 82.5 and 87.5 pounds. Given the current setting for the baler, what percent of the hay bales would fall in this range? ANSWER: % (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules) Sixty-seven percent of the hay bales should weigh below what weight? ANSWER: pounds (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules)

Answer 1

1) P(X > 90)

=P(=4, 40–4

=P(2272 90 – 80.5

= P(Z > 1.32)

= 1 - P(Z < 1.32)

= 1 - 0.9066

= 0.0934

b) P(X < 72)

= (A Par)

$= P\left(Z < \frac{72 - 80.5}{7.2}\right)$

= P(Z < -1.18)

= 0.1190

c) P(82.5 < X < 87.5)

= P(82,5 – < 45487.5.–)

182.5-60.0 87.5 - 80.5 =P( Z<- 7.2 7.2

= P(0.28 < Z < 0.97)

= P(Z < 0.97) - P(Z < 0.28)

= 0.8340 - 0.6103

= 0.2237

= 22.37%

d) (X < x) = 0.67

Or,P(X=4<==4) = 0,67

Or,P(Z < *780,5) = 0.67

Oh, 2 - 80.3 72 - =0.44

Or, x = 0.44 * 7.2 + 80.5

Or, x = 83.6680