Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 197 lb and a standard deviation of 40 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 lb. Complete parts (a) through (d) below. a. Given that the gondola is rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight is nothing lb. (Type an integer or a decimal. Do not round.) b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is nothing. (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 187.5 lb, which is the maximum mean weight that does not cause the total load to exceed 3750 lb? The probability is nothing. (Round to four decimal places as needed.) d. Is the new capacity of 20 passengers safe?Since the probability of overloading is

▼

over 50 % commaover 50%,

under 5 % commaunder 5%,

the new capacity

▼

does not appeardoes not appear

appearsappears

to be safe enough.

Answer #1

a)maximum mean weight is =3750/25=150

b)

for normal distribution z score =(X-μ)/σ | |

here mean= μ= | 197 |

std deviation =σ= | 40.0000 |

sample size =n= | 25 |

std error=σ_{x̅}=σ/√n= |
8.0000 |

probability = | P(X>150) | = | P(Z>-5.875)= | 1-P(Z<-5.88)= | 1-0= |
1.0000 |

c)

probability that their mean weight exceeds 187.5 lb

probability = | P(X>187.5) | = | P(Z>-1.062)= | 1-P(Z<-1.06)= | 1-0.1446= | 0.8554 |

Since the probability of overloading is over 50 % the new capacity does not appears

to be safe enough.

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a
mean of 201 lb and a
standard deviation of 42 lb. The gondola has a
stated capacity of 25 passengers, and the gondola
is rated for a load limit of 3750 lb. Complete
parts (a) through (d) below.
a. Given that the gondola is rated for a load limit of
3750 lb, what is the maximum mean weight of...

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a mean of
194
lb and a standard deviation of
37
lb. The gondola has a stated capacity of
25
passengers, and the gondola is rated for a load limit of
3750
lb. Complete parts (a) through (d) below.
a. Given that the gondola is rated for a load
limit of
3750
lb, what is the maximum mean weight of...

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a mean of
180
lb and a standard deviation of
37
lb. The gondola has a stated capacity of
25
passengers, and the gondola is rated for a load limit of
3500
lb. Complete parts (a) through (d) below.a. Given that the
gondola is rated for a load limit of
3500
lb, what is the maximum mean weight of the...

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a mean of 183
lb and a standard deviation of 37 lb. The gondola has a stated
capacity of 25 passengers, and the gondola is rated for a load
limit of 3500 lb. Complete parts (a) through (d) below.
a. Given that the gondola is rated for a load limit of 3500 lb,
what is the maximum mean weight of...

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a mean of
193lb and a standard deviation of 41lb. The gondola has a stated
capacity of 25 passengers, and the gondola is rated for a load
limit of 3750lb. Complete parts (a) through (d) below.
a. Given that the gondola is rated for a load limit of 3750lb,
what is the maximum mean weight of the passengers if the...

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a mean of 183
lb and a standard deviation of 40 lb. The gondola has a stated
capacity of 25 passengers, and the gondola is rated for a load
limit of 3500 lb. Complete parts (a) through (d) below.
a. Given that the gondola is rated for a load limit of 3500 lb,
what is the maximum mean weight of...

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a mean of
198
lb and a standard deviation of
3737
lb. The gondola has a stated capacity of
25
passengers, and the gondola is rated for a load limit of
3750
lb
b. If the gondola is filled with
25
randomly selected skiers, what is the probability that their
mean weight exceeds the value from part (a)?
The probability...

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a mean of
187
lb and a standard deviation of
39
lb. The gondola has a stated capacity of
25
passengers, and the gondola is rated for a load limit of
3500
lb. Complete parts (a) through (d) below.
Given that the gondola is rated for a load limit of
3500
lb, what is the maximum mean weight of the...

A ski gondola carries skiers to the top of a mountain. Assume
that weights of skiers are normally distributed with a mean of 186
lb and a standard deviation of 40 lb. The gondola has a stated
capacity of 25 passengers, and the gondola is rated for a load
limit of 3500 lb. Complete parts (a) through (d) below. a. Given
that the gondola is rated for a load limit of 3500 lb, what is the
maximum mean weight of...

8. A ski gondola carries skiers to the top of a mountain. It
bears a plaque stating that the maximum capacity is 13 people or
2132 lb. That capacity will be exceeded if 13 people have weights
with a mean greater than 2132lb/13 = 164 lb. Assume that weights of
passengers are normally distributed with a mean of 181 lb and a
standard deviation of 40.9 lb. Complete parts a through c
below.
Find the probability that 13 randomly selected...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 25 minutes ago

asked 32 minutes ago

asked 32 minutes ago

asked 53 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago